Whether she requested it first or not, Tasha's orders would have been to go the Ent-C. There would have been a crew transfer process, this would technically be "an order". Picard allowing it to happen on his watch makes him the responsible party for the repercussions. So the statement isn't wrong, it's just a question of how you interpret it.
Again, Guinan is
not a superior Starfleet officer but Picard's friend. There's no record or hint in the series that she handles things from a military perspective and her message and sour face ("sorry to be the one having to tell you this") clearly suggests that in yet another (unseen) parallel time line or universe Picard
did "send" Tasha to the past and therefore "is responsible" according to the undersatanding of normal people.
The series was not made so that for the decades to follow we'll twist every bit of dialogue out of the original context which general audiences were enabled to understand.
Obviously, it's not an elegant piece of retconning, and it could have been avoided, but it's preferable to the alternative in this case.

Why is it preferable to retcon Andrew Probert's
Enterprise-C design on the conference lounge wall as non-canon? (by insisting the Sternbach design is the only one "real" in our universe) It's been there for four seasons of TNG, prominently displayed above the actors and captured in many scenes.
Be honest: would you be making these same conclusions if you disliked the Probert design?
Unlike some of our "experts" (i.e. deliberate ignorance of the Romulan Star Empire crest featured in "The Enterprise Incident" and "The Neutral Zone") I'd like to think I take treknological research rather seriously and take the onscreen information into account on an unbiased basis, but with the prerogative "first come, first served".
Had it been Rick Sternbach's design on the conference lounge of the "D" he'd equally be entitled, that we first look for imaginative rationalizations
before we push his design over the cliff and deem it "non-canon".
It's no secret that I do have an infatuation for Andrew Probert's design, a "continuity freak" in the most positive sense of the word and someone I consider my mentor. This apparently was a motivation that did help to examine the information from "Yesterday's Enterprise" and its changed premise because of "Redemption II" which I unfortunately overlooked in the first parts of the treatise / this thread (Hopefully someone would have noticed it eventually).
Except it's not preferable to you because you are intent on clinging to the idea that the Enterprise-C design is different. That's what it comes to: your preferences and desires are fueling your "evidence". These are not conclusions that are naturally and logically reached, they are grasping at straws to justify a preference. It's a classic example of confirmation bias.
No, it is not. From what I read here, it's that "fans" are not willing to take the (new) information from "Redemption II" into account and discredit it (so that the assumption that turned into a myth can remain some kind of "truth").
Alright, then
I'll bring in my last two witnesses, the screenplay writer and director of both "Yesterday's Enterprise" and "Redemption II", Mr. Ronald D. Moore and David Carson.
Mr. Moore, I understand that the core theme of "Yesterday's Enterprise" was "meaningful death", one as a justification for the crew of the
Enterprise-C to sacrifice themselves to prevent a war costing 40,000,000,000 lives, the other one for the character of Tasha Yar to ask her leave and be assured of a "meaningful death" she didn't get on Vagra II in "Skin of Evil", is that correct?
Ronald D. Moore (screenplay writer):
"We brought Denise back to kill off Tasha Yar a second time. It was a great opportunity to send the character off in a big heroic sacrifice because nobody was really happy with the way she left the series in the first season. Nobody on the show really liked it, the fans didn't like it, I'm not sure even she really liked it. So 'Yesterday's Enterprise' was a chance to kill her right."
David Carson (director):
“I think it was terrific to bring her back and have her die meaningfully, and give her a good reason to leave.”
Mr. Carson, this is essentially what you said in the "Alternate Lives Part I" documentary from 2008, is that correct?
[David Carson would have to reply "Yes"]
So, by 2008, Mr. Carson still felt that they had given the character of Tasha Yar a meaningful death in "Yesterday's Enterprise"?!
Sorry, this doesn't add up.
Mr. Moore and Mr. Carson collaborated for "Redemption II" and I only see a meaningless death for the character of Tasha Yar, unsuccessfully trying to escape with her daughter and being executed after having been caught. What's "meaningful" about this kind of death? (At least, on Vagra II she did in the line of active duty and on her feet but not tied down for some form of execution).
A few months after “Redemption II” had aired, this is what director David Carson (then) had to say:
“I particularly liked the challenge of “Yesterday’s Enterprise” because we were creating the Enterprise in a different and parallel time line: An Enterprise at war.” (Starlog ST-TNG magazine Vol. 19, Spring 1992).
A "parallel time line" is not "our" altered time line, it's parallel to ours, and as such it is practically indistinguishable from an alternate universe.
This clearly indicates a logical premise change:
You can't have Tasha Yar die a meaningful death in (the past of) "our" universe and at the same time bear a daughter in (the past of) "our" universe and later die a meaningless death.
Either she died a meaningful death in our universe or she did NOT die a meaningful death.
Obviously the only way to resolve the problem was to relocate the (parallel) events featured in "Yesterday's Enterprise" into a
parallel time line (David Carson) aka a parallel or alternate universe.
And Moore and Carson elegantly avoided to explain the various inconsistencies and oddities I've mentioned throughout this thread / treatise, necessary to explain before even coming up with the assumption that "Yesterday's Enterprise" Tasha travelled back to
our universe.
Apparently Ronald D. Moore deliberately and consciously made [another] Picard sent [another] Tasha Yar to the past with the
Enterprise-C which inevitably
must have taken place in another (unseen) alternate universe and thus created a believable context so that Tasha could somehow give birth to her half-Romulan daughter Sela (instead of rotting in a Romulan detention cell with all the Federation technology information in her head which would have been the likelier outcome of her travelling to the past and being captured by the Romulans instead of being killed at Narendra III).
And from a story-telling perspective it’s totally irrelevant,
who sent Tasha Yar back to the past and
is responsible. Guinan could have just said “And I think I sent her there. I just know I did. If I’m right, then I am responsible for this whole situation”.
We are apparently looking at a (too) subtle suggestion of Ronald D. Moore that the events of "Yesterday's Enterprise" had been relocated into an alternate universe by the time of "Redemption II" which previously no one noticed.
I'd suggest we better deal with it, rather than to come up with all kinds of convoluted theories why that shouldn't be the case and stop discrediting the characters and people concerned unless you really want to read the vitriolic satire
The Enterprise-"C"onspiracy I wrote over this weekend (from a strictly Cardassian point of view).
And so from February 19, 1990 (airdate of “Yesterday’s Enterprise”) until September 23, 1991 (airdate of "Redemption II") Tasha Yar had a meaningful death in the past of
our universe – and the Enterprise-C of
our universe apparently looked like the starship featured in “Yesterday’s Enterprise” (a remarkable cosmic symmetry and irony: these events in “our” universe were almost as short-lived as the “universe at war” itself, featured in “Yesterday’s Enterprise”

).
Bob