I believe they meant fake jesus in the sense of 'false fulfilling of prophecies'.
Additionally, it's so old, and if you managed to convince people you were the Son of God (regardless of whether you yourself believed), and the human conscious mind essentially developed to rationalize events and justify itself to others, then you'd probably look at the old prophecies, find the parts you fit, say "look, see!", and for the parts you didn't fit, either discredit the author/find reasons why his stuff was actually heresy, or interpret it in more creative ways until you did fit, then have them revise the text to be more clear about what the prophecy was actually about.
This doesn't even look like scamming, from the inside. You don't realize you're doing it. You're obviously the Son of God, that guy just happened to wrong, might not have been his fault, he didn't realize it was actually the Devil deceiving him into believing that he'd been given a prophecy. You can't blame him for having been false. I mean, sure, you can't use his work since it's still heresy, but his predictions obviously didn't come to light when you were born...
For other authors, maybe they were just really unclear about what their prophecy meant,or were being metaphorical but it's not immediately obvious. I mean, if you look at it from the real perspective you should look at it from, then it makes sense and is both supported by the evidence that you fulfilled that interpretation, and supports the fact that you are the Son of God.
If I thought I was the Prophet come to Lead the People to the Promised Land? I would totally do that. It wouldn't be on purpose; to me, this would just be the self-evidently correct way.
Oracles, prophecies, and predictions are tricky things. There's a reason they tend to be as vague as possible; the people who don't like you/your method will just think you got lucky or that it happened for a different reason than you said it would (obviously invalidating/not providing any evidence for your ability to see the future/predict the market/speak with god) anyway, the people who support you will be disappointed if your wrong, you'll be disappointed if you're wrong, but if you can justify it to yourself that you sorta kinda predicted it if you look at this way, you won't feel as bad, your supporters won't feel betrayed, the opposition will just grumble about you being vague and this being kinda dumb, and so on.
The more vague the prediction, the more likely it is to be able to be interpreted as accurate. If it can be interpreted as accurate, it's more likely to survive the test of time. If someone makes a lot of vague predictions that are wrong on the surface but can be interpreted as correct, their legacy will live. If someone makes a lot of precise predictions that are right sometimes and wrong sometimes, they're obviously unreliable and the predictions they made are just noise, not signal. Even someone who's really good at prediction screws up sometimes, simply because humans are fallible, and don't always have all the information. But their opponents will leap on that every chance they get to tear them apart. If they're vague, instead, then while it doesn't give much useful information, it's much easier to justify after the fact, whatever happens.
Similarly, trying to act on precise prophecies and oracles screws up the whole process that predicts them. It either becomes a self-fulfilling prophecy, or maybe it's in a field where making predictions actively reduces the predictability (markets is the example of this I read of), or it causes the prediction to be false where it would have been true if you'd never known. "You're about to walk off an invisible cliff." You stop walking. The prediction is now false, because it was expressed. Trying to say "I knew all along!" to avoid this carries it's own problems that should be immediately obvious.
The real tale of Oedipus is that using predictions to make decisions can have dire consequences if you don't take those decisions into account for the prediction. At least, in this context. Perhaps if it was interpreted differently, you could find something else that's true....