"Parody is fine as long as you don't actually use somebody else's logo. That crosses the line from fair use into trademark infringement."

I don't think that's entirely true. I believe you can use a trademark in a parody, but you should be sure your work actually falls under the legal description of a parody, i.e. it makes a critical commentary or statement about the original work. It isn't enough to just be funny.

'course, ianal.