While I was working on my MLIS, I worked reference at a large urban college in the Metro-Detroit area. One of the absolute craziest reference questions actually started as the most innocuous:
"Hey, where can I find this woman?" The gentleman in front of me was holding out a student ID card with a name and face... neither of which could be even remotely considered his.
While I explained that we couldn't give out that information - even if we had access to it - another patron came up to the desk. She waited patiently for a few moments, and then turned abruptly towards the first patron, "Hey, that's my ID! You broke into my car last week and stole it!" I believe the probability of this occuring was 1 in 3.7 trillion.
While not admitting that he had, indeed, broken into her car while it was parked on campus, he did try to sell her the ID back - right in front of me. I remember that he also said that he had to feed six children, thus the need for her to buy back her ID.
I offered to call security - the ID was promptly returned (while the man ran for it).