Yep, pretty much. The basic facts (Trip sacrificing himself, Archer and crew still around in 2161) are probably still true, but the details are probably dramatized quite a bit, maybe even extensively. I see Riker's program as a gross dramatization, perhaps meant for children, and not historically accurate (because, of course, it has to have narrative structure to fit Riker's presumed timescale). Certain things like the Trip-T'Pol relationship, or correct ranks, may have been glossed over in favor of the idolized NX-01 crew (as they were at the start of their launch in 2151) placed in this adventure at the dawn of the Federation (when they, historically, may have actually been footnotes or washed-up has-beens).
2370's "Archer vs. the Rigel X Gang!" may have been historically as accurate as 1960's "The Alamo" (which might be what O'Brien and Bashir are cosplaying around the same time on DS9). We know in the same time period, the Doctor can make a pretty good living (er, uh...) by grossly fictionalizing his own crew on Voyager. I'm sure the 200-year-old dead have even less personality rights.
TATV is a deeply misunderstood episode. I think the lesson TATV tries to teach is that nothing is as how it seems.
Reed probably did get promoted to lieutenant commander, & Sato and Mayweather probably did get promoted to lieutenant junior grade by 2161. It just does not appear so in the finale, even though Captain Hernandez is shown to be calling her helmsman a lieutenant when Columbia launches earlier in the season. Making a single pip associated with both ensigns and junior grade lieutenant ranks to be canon. And opening the door for dual pips to be associated with both lieutenant and lieutenant commander ranks. As hollow pips don’t exist at this point.
Trip probably did not return home, but he did not really die either. It was just written into the program that he died. Since his actions when the pirates board Enterprise can be construed as both munity and staying loyal to his captain. Which would have been based off of records from the Enterprise, which Reed would have access to, being the security officer after all.
And although never mentioned, Reed – in addition to his ties to Section 31 – is technically the second officer on Enterprise due to Trip transferring to Columbia earlier in the season. All Trip did when returning to Enterprise was become Chief of Engineering again. It was never acknowledged that Trip was made second officer again when he returned.
We see no MACOs come to Archer’s and Trip’s rescue despite being present for the Rigel X mission, but again, that what was written in the program.
Even the discussion that T’Pol and Trip is not what it looks like. It’s taken at face value as meaning different postings on starships, and not as meaning that it’s already been decided that Trip has already been assigned or recruited to work for Section 31. Meaning when the pirates are able to catch up to Enterprise to dock and board it, T’Pol is just playing her part allowing them them to do so. And Trip probably took the pirate’s ship afterwards for his assignment.
And since Shran faked his own death years earlier, its possible that Shran was in on it too.
Also, clearly, at no point are Romulans mentioned at all by any member of the Enterprise’s crew. Even though the Earth-Romulan War is a very recent event. And would be the most likely reason that Enterprise is being decommissioned after ten years even though its known that Enterprise was built to last over a century, according to “E2”. Yet, the subplot of “The Pegasus” involves Romulans searching for the Pegasus.
And the events in the episode “The Pegasus” is something that Starfleet intelligence was watching closely.
The holo-program itself is not beneficial in helping Riker talk to Picard in the slightest. But it could have been useful for Riker to stand up to Pressman, his former CO. Archer isn’t in command of Enterprise anymore during TATV, as it was decommissioned in 2160, as seen in Archer’s personnel file in IAMD. Technically, making him Trip’s former CO.
The uncertainty regarding the truth of the final week of Enterprise does fits into the first half of “The Pegasus” and the uncertainty surrounding the Pegasus if watched again and TATV is the back of your mind while watching.