1. (Almost) all beliefs are based on appearances. (Exceptions: faith, self-deception.)
2. A belief is justified only if it is based on something that is a source of justification.
3. Therefore, there are justified beliefs only if appearances are sometimes a source of justification. (From 1, 2.) (Faith and self-deception are obviously not sources of justification.)
4. If PC is false, then appearances are never a source of justification.
5. So if PC is false, then no belief is justified. (From 3, 4.)
6. So no one is justified in believing any alternative theory to PC. (From 5.)
I'm not sure that (6) follows from (5). Some philosophers who either haven't seen or aren't convinced by Huemer's argument may find that some alternative theory X seems right to them, and if PC is true then this undefeated appearance can justify their belief in X. But never mind that: the conclusion in (5) is strong enough to establish PC (just tollens on the further premise that some beliefs are justified).
A more serious flaw, I think, is premise 4. I think the most plausible alternative to PC allows that appearances are sometimes a source of justification. It just adds a further objective constraint: the content of the seeming must not be objectively crazy. This alternative view yields more plausible results than PC when we consider severely incompetent agents. PC seems to imply that any proposition whatsoever can be justifiably believed: it merely requires that the proposition seem true to the agent, and that they not have any other relevant seemings (which could potentially serve as defeaters on Huemer's view). But severely logically confused agents (for example) should not qualify as having justified logical beliefs. If it seems to you that 2 + 2 = 4, and it seems to me that 2 + 2 = 99, these two beliefs are not equally rational or justified -- even if we both have equally strong-seeming intuitions. In this case, your mind is functioning properly and mine isn't: my belief is just crazy, even if it doesn't seem so to me from the inside. As I keep saying, one can be irrational without realizing it.
So, this strikes me as an appealing alternative to Huemer's view which isn't undermined by his self-defeat argument. Intuitions justify, except when they're objectively crazy. We may add that the previous sentence is not itself on the list of 'objectively crazy' claims. Hence, if this view is true, then those who find it intuitively plausible can justifiably believe it. It isn't self-defeating. (One may be suspicious of the notion of 'objective craziness', and so reject the view on those grounds. But that's a different objection.)
[Disclaimer: As always, I'm not making any claim to originality or uniqueness here -- several others in our seminar seemed to be thinking along similar lines.]