Here again is how Harry Frankfurt formulates the principle of alternate possibilities in his 1969 J. Phil. article:
PAP. A person is morally responsible for what he has done only if he could have done otherwise.
It is now time to put 'could have done otherwise' under our logico-linguistic microscopes. The phrase is ambiguous. On one reading, 'could' is the past indicative of 'can' where 'can' signifies ability: If I can do X, then I am able to do X. Accordingly, if I could have done otherwise, then I was able to do otherwise. Suppose I failed to lock the door last night. Then to say that I could have done otherwise is to say that I was able to lock the door last night. So, on the first reading, 'could have done otherwise' means 'was able to do otherwise.'
On a second reading, 'could have' is a past subjunctive form, and so 'could have done otherwise' means 'might have done otherwise,' where 'might' is used nonepistemically. There are epistemic and nonepistemic uses of 'might.' Here is an example of an epistemic 'might': 'I might have locked the door -- I'm not sure.' The idea is that my having locked the door is consistent with what I remember. But the 'might' in 'I might not have existed' has nothing to do with knowledge or ignorance. The idea is rather that, though my existing is actual, my nonexisting is possible, which is to say that my existing is modally contingent. This has nothing to do with knowledge or ignorance. It is an ontological claim about what is (broadly logically) possible.
The foregoing suggests the following disambiguation of PAP:
PAP*. A person is morally responsible for what he has done only if he was able to do otherwise.
PAP**. A person is morally responsible for what he has done only if he (nonepistemically) might have done otherwise, i.e., only if at the time of the action the agent had available to him a plurality of alternate possibilities.
The difference between the two principles is that the first is consistent with the truth of determinism, while the second is not. For if determinism is true, then at any time there is exactly one nomologically possible future. Determinism thus rules out alternative possibilities, and with them PAP**.
How is PAP* consistent with determinism? Well, if I was able to do X yesterday, that could be construed to mean that I was able to do X yesterday had I wanted to do X yesterday. My ability so construed is consistent with the truth of determinism.
Which of these two principles did Frankfurt have in mind? The fact that he employs the label 'principle of alternate possibilities' suggests that he had PAP** in mind. But his counterexamples, if they work at all, would work against PAP*.
So I'm not sure what he had in mind. One thing seems clear, though: to evaluate a putative counterexample of PAP we must know what exactly PAP is.