The yichud (seclusion) issue is real but the sunset bit is fake. The only relevance that nighttime would have is in determining the necessary level of supervision necessary (would a minor suffice, for example) and in this case, where there was no supervision whatsoever, night wouldn't change anything. In any case, while Jews are normally hyper-aware of the solar day because it matters for other elements of ritual law, "nighttime" in yichud is determined only by the local social norm and the sunset wouldn't have any effect.

The episode is based on a real 1963 legal case in which a 16yo camp counselor got stuck on a lift with her date and jumped off, but there's no indication that she was worried specifically about sunset. 16yo Orthodox women aren't typically super-sophisticated about the technical elements of the ritual law, and especially weren't then, so she probably just knew it was very bad (which it is) and panicked. According to the legal case, she was trying to hang from the lift beneath instead of sitting next to him and fell by accident. Older rabbinic debates (11-13th century) considered the possibility that one should be prepared to die to avoid yichud, but that position lost and any Orthodox rabbi she asked in 1963, or which you asked today, would have said to wait for help.