When a file format starts at offset 0, it simply means that it starts at the first byte of the file.
Other than that, I can't provide any information on file formats allowed to start at offsets other than 0, or why this may or may not be a good idea (I suppose maybe it would allow an enterprising programmer to hide a malicious file by embedding it in an otherwise-innocuous format?), though I am certainly curious as well.
I think you're on to the right answer (though I don't know for sure myself).
It seems to me that if all file format identifiers started at the zero offset, it would be impossible for a single file to identify as more than one format. However, when different formats use different offsets to identify themselves, it is possible to construct the file in such a way that it validly identifies as more than one format.
That's kind of a different issue though, my understanding is that .jpeg has an unlimited size footer and .rar has an unlimited size header. It gets similar results, though.
Other than that, I can't provide any information on file formats allowed to start at offsets other than 0, or why this may or may not be a good idea (I suppose maybe it would allow an enterprising programmer to hide a malicious file by embedding it in an otherwise-innocuous format?), though I am certainly curious as well.