I believe [PA] is consistent with itself, yes

Can you tell me your basis for this belief?

Your analogy fails, because PA and the toy system both agree in describing 0 and 1 as next to each other. But PA asserts that 2 is next to 1, while the toy system explicitly denies that it is so. The map of Europe doesn't in fact make a claim about the existence of Washington; it just says that if it exists, it's outside the map. But the toy system makes an explicit claim about the number 2. It's not that it's outside the range of the system; the system aggressively asserts that it covers the place where 2 would be if it existed, and also that there ain't no number there.

Answered here.