Here are some possibilities where Billy isn't a goat:
- No one actually pays attention to Billy and helps him get off where his sign says
- The train goes to the wrong place
- The destination is something like a circus and it's no longer in town when Billy arrives
- Billy eats the sign despite being a human (he's only 4)
And my favourite possible explanation: he's holding the sign upside down, unaware that it spells something different that way.
You doubt me? Okay, since sending kids on trains is typically a British thing, let's say he's going to Wales. He drops the sign at some point (work with me here) and ends up holding it upside down. As a result, the adults misread it, and he's taken to Salem and burned as a witch.
Not so funny now, is it?