Keep in mind my question is about the general ability to use a "lack of knowledge" claim to invalidate a positive claim. Determinism/apple pies are just examples.
In that case, let's start with your specific examples, and then move on to the general case.
You claim that:
I don't see how my uncertainty about the nature of the apple pies has any effect whatsoever on the actual possibility of the composition of the pies. Either the apple pies are made from handpicked apples, or they aren't. My uncertainty about it does not make either possibility more or less probable.
And this is true--of apples. Observation of apples has no significant effect on apples.
Things are different at the quantum level, however. Observation of particles has a definite effect on the particles. Thus, any notion of determinism that relies upon the observability of particles has a problem, as the act of observing interferes with the experiment (and may alter what would have occurred had the observation not taken place.) So, certain attempts to demonstrate determinism are stymied by the uncertainty principle.
So, from there, we can move on to the general case:
My question is in reference to people who hold that the lack of complete understanding in a particular field can invalidate a positive claim.
The answer is that this can occur only in cases where "the lack of complete understanding" is of a structural (i.e., transcendental) nature and not of a purely contingent or accidental nature. In other words, where we are dealing with situations where X is viewed as a necessary condition for the possibility of Y, uncertainty about X can invalidate positive claims about the presence of Y.
In practical terms, you're unlikely to run into this problematic outside of the quantum level, or other unusual edge cases.