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.