To be honest, sending e-mails from any e-mail adress is extremly easy, so it's not that hard of an attempt to make. The problem is anyone answering this e-mail will write to the actual professor who would then notice the scam (if you're stupid enough to add the teacher to the mail-list then....).
It's however not a stupid attempt, if you do it on a such enough notice that the teacher isn't made aware, and most students believe then they will have no choice but to give the whole class a second chance, as they can't fail the students that believe in it.
And making it in an untraceable way shouldn't be too hard, using a proxy, and perhaps a public computer.

This popped up a while back, and some good comments defending the teacher were actually given, so here goes :
Unless the dude can have his method for solving the problems proven to work in EVERY case (every single one, no exception), and have that peer reviewed then he can't use his method. Maths is a lot of small tools and rules that you add together to make complicated stuff, his method might work for now, but how will it behave when you start doing more complex things ? Because if you can't use it then, then not knowing the 'official' method will become a real problem.
Now it might be a bit harsh to fail him, since if he did come up with his own method the dude just might be a genius, but it's not all black and white as you all seem to mention.
If a teacher fails you because you used a different method than the one taught in class BUT that other method has been proven to be equally valid then the teacher is a bad teacher. But that's a BIG but.

Except if someone is goddamn late I'd rather they apologize for being late than thanking me for being patient....