There's a Capitol train about ten minutes after the ACE comes through. That's one of the reasons the ACE train operators make so many "Not Amtrak" announcements. A few miles east of Fremont, the tracks diverge and ACE heads east toward Pleasanton and Stockton while the Capitol turns north toward Oakland and Sacramento. And ACE only runs one direction. Basically, if you get on the wrong train at Fremont, you're stuck.
The family seemed only vaguely aware of the local geography. One of them said, "Why can't she just get off the train at Tracy and ride BART back here?" (I don't know how she got the idea that BART runs to Tracy.
Also a problem here is that Amtrak and ACE tickets aren't interchangeable. Technically, the woman who got on that ACE train without an ACE ticket could be subject to an expensive citation, since ACE doesn't sell tickets on the train — they're a "proof of payment" system where you pay in advance and if you ride without a ticket you receive a citation for a lot more than the ticket costs. I suspect that in practice the train managers get this situation quite a bit and didn't cite the girl, but would make her get off at Pleasanton, the next stop. No matter how hard you try to explain it, trains are such rare, odd, unusual creatures that many people don't seem to understand that they don't all go to the same place.
Anyway, what the family seems to have done was to call their wayward member and tell her that one of them would drive over to Pleasanton and bring her back to Fremont, where she could catch the last train of the day from Fremont to Davis, and at that hour, there wouldn't be ACE trains running so there's no chance of getting on the wrong train. Unless she got the platforms confused and didn't read the destination signs on the side of the train and got on a San Jose-bound Capitol instead.
I have saved people from getting on an ACE train or the wrong-direction Capitol more than once at that station. People really need their hands held. They don't listen to announcements and they don't read signs or train-destination placards. And Fremont station, even with only two tracks, can be confusing because the platforms are not directional. A train going either direction can call on either platform, although there are normal calling patterns. However, you can't always rely on it, and there's no guarantee that "all trains to Sacramento stop at platform 2" or anything like that.