No. For that attack, the code that is speculatively executed does need to be in the target context, but that doesn't mean the code has to be attacker-supplied

No. For that attack, the code that is speculatively executed does need to be in the target context, but that doesn't mean the code has to be attacker-supplied (that just makes it easier). It's also possible to use existing code in the target context as the speculative execution path if it has the right form (and this is what P0's Variant 2 POC does, in that case by poisoning the branch predictor in order to make it speculatively execute a gadget that has the right form).