Makes sense to me, and if SBF was as smart as he thinks he is, he should have thought of this possibility. Why would an individual think they have any authority to enforce an extradition agreement made between two countries? Completely nuts.
This is not a crazy as you seem to think, and, in fact, if they cannot, this is a fairly recent (last 30-ish years) change in the state of the law. As the Supreme Court noted in U.S. v. Alvarez-Machain (1992), at that time, prosecution in violation of extradition agreement was invalid and the defendant absolutely could raise this issue independently. (A protest from the other government party may or may not, depending on the extradition agreement, be a factor in whether the prosecution is in violationof the agreement, but that’s a different and treaty-specific question, apart from whether or not an individual charged has the right to raise the invalidity of the prosecution under the treaty.)
2. He probably wanted out of the prison he was in.
3. He's out on bail right now, so he's got that going for him.