In this world the government had a super soldier program that was not a secret, corporations that have CEO/Presidents as heroes (Iron Man) & villains (Green Goblin).

So if believing the sickness gave her powers is perfectly reasonable, then the only plausible explanation is cosmic radiation, mutant, government, or corporate.

She knows she isn't a mutant and has never been in space, that only leaves government or corporate. Unless you want to create random spontaneous mutancy in nonmutants or cosmic radiation storm on Earth that somehow never made the news as legitimate & ludicrous things then be my guest.

Until you can provide a "better" option for her to believe then it is staying.