This has all sorts of intriguing implications. People don't seem to realize the extent to which math is horribly limited. Math is a description of the reality we perceive. The idea that any mathematical construct is somehow 'right' in the absolute sense is, almost in a definitional manner, a flawed idea. Alter the brains of humans and you will see the rules and 'definition' of math change accordingly.
0! is defined to be 1.
When something is defined to be a certain way it just is. Its not right or wrong, true or false. It is what we use to determine if something else is true or false.