"Can I e-file their taxes as self-prepared by them?"

Isn't that being not quite honest?  I understand that people that don't tell the truth can sometimes get in trouble with the law.  As a side note, do those states require certain licensing or are there some exceptions?

That's way I am confusing if I can and should to do it. They said it was easy and they did this on the paper but they want to e-file. 

I don't know about any exceptions because I never checked it. 

You might want to check.  It's better to take the high road than the low road, even if the high road has a couple of detours in it.