Yet it had been stated many times, on both TOS and TNG, that record-keeping from that era was at best incomplete, and unreliable.
Many times? No, the only time I can think of that this was ever mentioned was in "Space Seed," and Spock was referring to the 1990's not the 2160's. And for having "incomplete" and "unreliable" information, Riker's holodeck program sure was amazingly accurate in its presentation of the NX-01 crew and the NX-01's surroundings. Those people looked, talked, and acted just like they did in the 22nd century.
And there is no reference to her having done the research you speak of. She may have taken the revelation in the holonovel at face value, even if records contradicting it were readily available.
There didn't need to be a reference. I don't have to do any research to know that Abraham Lincoln was shot and killed in Ford's Theater. That was something I learned in the course of my life. This is no different. If someone was reenacting Lincoln's life, then he better end up dead in that theater, because that's how he died in real life. So if Riker was reenacting the events taking place on the NX-01 before the founding of the Federation, then Tucker better die in the manner he did, because that's how he died in the "real life" of Star Trek. And TATV never once gave the impression that it was a "holonovel" (i.e. that it was just a fictitious story about the NX-01 crew), and gave every indication that these events actually happened.
And before I make a huge deal out of this, I'd like to say that I'm not sticking up for TATV, or the silly way Trip died. I think TATV is a pile of garbage, but its writers and producers did not intend for it to be a fictitious holodeck fantasy.