Its not terribly uncommon at least around here for an agency to have a number of NFA firearms. Some were purchased or they were given to the particular agency prior to the 86 ban, and they registered them in such such a way that they can not be transfered to non-law-enforcement.
I know of a couple of dealers that went out of business who "donated" the post-86 items to an agency as well. Some agencies just keep them locked up and they gather dust for the most part, but I guess its better then having them cut up in some ways.
The military did loan out a good number of m16's and some m14's through a law enforcement assistance program, unsure though what is currently available.
Just in case some are curious as to prices for some of these law enforcement firearms just do a google search. Here is a couple of flyers from the last few years.
With 1919a4 for $250.00, Colt m16's for $500.00 (btw this is a high price) etc.
Multiple Ak varients from $200-$250.00 and other various things.
Law Enforcement only NFA weapons just dont seem to bring much money at all, so they tend to get just tossed in the back of the safe and almost forgot.
I do agree that some of it is overkill, as can be seen in the self propelled howitzer that Sheriff Joe has.