Definitely, run that vehicle identification number FIRST!!!
A good while back I purchased a B-body donor shell that was advertised here on Moparts. Looked too good to pass up and was sold on a bill of sale, but turned out to be STOLEN.
Anyway, I did the right thing and had my local sheriff come and impound it.
It took over a year of waiting and paying prorated impound storage $$ to get it back. Even then, if the person who reported it stolen wanted to claim it, they'd have the right to, and I would have been out of luck.
Not saying that all bill-of-sale only transactions aren't valid... just remember the advice from the first line of this post!