The reason the lender wants it documented is that federal law gives them the right to file for a special type of mortgage lean, called a "preferred mortgage" -- on federally documented boats. This is from the Coast Guard's FAQ page:
"WHAT IS A PREFERRED MORTGAGE?
A preferred mortgage is a mortgage which is given status as a maritime lien. As such it enjoys a certain priority in the event of default. In addition, the Coast Guard is prohibited from making certain changes in documentation including, but not limited to, change of vessel ownership, name, and hailing port without consent of the mortgagee. For this reason many financial institutions require vessels which are eligible for documentation to be documented and to have preferred mortgages recorded against them."
To figure out whether your boat qualifies (and the only requirements are that it be owned solely by American citizens and be at least 5 net tons in volume) try the form at this link:
http://www.uscg.mil/hq/msc/T3/cg5397/cg5397.form.htm
Have fun,
Rick