@Veektarius: I'll see what I can find. The collegiate classes I took where I had to write papers had professors specify that "based off" was not correct. I'm not sure if it's in Strunk and White or whatever, but googling some college websites led me to this (I went to TCNJ, not WSU, if that means anything) and some Mirriam-Webster thing that doesn't say it's wrong just frowned upon (not that it matters what they say, OED for life!). Certainly "off of" (as most use it) creates a needless preposition. "I jumped off the building" is simpler, cleaner, and quicker than "I jumped off of the building."
Using two prepositions back to back is not improper (though I imagine the "off base" part does make a good deal of sense and I would need to look at a few grammar rules and linguistic history to really prove that it's incorrect), but it seems that the definitions do clash with one another.
That said there's the case to be made that language is constantly changing (it is), and as long as we understand what another person means/usage becomes common enough then prescribed codes become even more irrelevant (they do/are). So really it doesn't matter if I say "I spoke to my friend" or "I worked to my friend" if the majority of people understood "work" to mean the same thing as speak rather than what work is generally accepted to mean, regardless of any fixed definitions.