Does this really mean "any," as in "I'll read any of her books," or does it reLly mean "not any," which is to say it means "any," but only when that word appears in a negative sentence?
Nope, "dim" means not or no. "dim byd" would mean "not any". Looks like an error.
The meaning of dim varies with the context. There is no context here, so it could mean any of a number of things - not; anything; something; nothing; none; nil; ...;
www.gweiadur.com shows a long list of expressions involving dim which is worth a look.