The Writer's explanation is actually not inconsistent with past depicted time travel.
Truth be told, it shed further light on what these Time Travel stories may have ACTUALLY done.
Second, the MWI interpretation of Time Travel as depicted in the movie can only be explained so far.
Also, there are many items that support it, including the scene where uhura states "An Alternate Reality", whereas nothing on screen CONTRADICTS it.
Therefore, it is the case.
Yesterday's Enterprise establishes that in THAT alternate reality, the was for the Federation was going badly, and that they would loose.
Not an SOP, just Picard's thinking at the time.
Also, MWI could only be proven by observation, and I remember a story about a cat in a box.
Going BACK in time, you create an Alternate Reality, FORWARD trips do not, so whenever someone has gone back in time, and thus created a new reality, the time traveller sees no sign that a new universe is created. Moving Forward in time is much simpler, since we do that anyway, just maybe not as fast.
If the Timeline is assumed to be ERASED when the Narada starts changing things, then Spock and the Narada would have to be radically altered by such changes, aka the Grandfather Paradox, and thus events in the movie would be simply impossible.
Therefore, MWI is the truth left after eliminating the impossible.