"He probably doesn't have enough credibility" bro the photograph? The knowledge of how his power works? He can prove it to anyone else as easily as he did to her.
If anything it'd be better to argue he knows he's dying regardless, since he said his power is irrefutable and doesn't give a shit about anyone else in the school than that people wouldn't believe him.
I think him not giving a shit about the others is totally plausible, half the premise of the series is that these little shits can end up with a bunch of hubris, and realistically a lack of empathy, but the better reasoning is right there.
Anyways I think this series is fairly neat, like it more than the average commentator does, but it definitely has a good couple holes as well as weird actions.