Someone who wakes up and ha sno idea who they are or what their age is, is creepy. If that particular someone is a demigod, it practicly screams out "MAGIC! SOMETHING GODLY! NOT RIGHT!"
I have my own little ideas on what's up with Jason... (some of them I have heard on this particular spot actually)
1. Jason took a dip in the Lethe. As you might recall from the sword of Hades, taking a dip in the Lethe is not that great of an idea. You forget who you are ect. Jason might've been summoned/dragged/lost in the Underworld and by an infortunate mistake, fell in the Lethe. Hades (not likely), Persephone (she does like heroes), Nico or anybody else with a friendly mind down there could have retrieved him and brought him to the normal world. There, he would've integrated him in a normal school, knowing campers were on their way to that school and waiting for that, they mistified everyone. Including the school satyr, Gleeson Hedge.
But I don't think satyrs can be affected by the msit, so unless Gleeson was there at the Lethe as well, or just pretending, this theory is unrealistic. Plus, he wasn't wearing armor or camp shirt when he woke up, (which campers wear during missions, but new clothing is an easy problem) and it doesn't explain how he got in the bus by himself (if he would've just popped in the bus it would've been mentioned). But of course, mist does magic.
2. Jason stayed in the Lotus Hotel and Casino too long and forgot his own identity and was retrieved during his sleep or something and brought to the Wilderness school, where the students and staff were mistified. It still doesn't explain why Gleeson knows Jason does not belong, and this setting was used a lot in PJO and I doubt it would be granted such an important spot once again. Like said, Rick doesn't like to repeat himself.
3. Some god, Jason's parent perhaps, interfered in a close call with a monster and just placed Jason safely in a bus. To cover up, he misted everyone there. But satyrs aren't affected by mist, which is part of the reason why they find monsters, so like alot of my theories, it doesn't make sense. Plus there is te "no direct intervention rule"
4. Jason messed with a certain titaness of memory. Maybe Gleeson Hedge tried to stick up for his protectee and Mnemosyne did a double job. This explains why he has a distant memory about the coin/sword in his pocket. Of course this theory does not explain how he suddenly got in a bus, but titans do have magic.
Most of theese theories have a flaw to them and are probably unrealistic (even for a fantasy novel). Of course the writter is Rick Riordan, so the possibility is immense that none of the theories are right and Rick pulls out somme Myth nobody knows but that makes perfect sense.
