There are plenty of military assigned to NSA, to do things like operate SIGINT aircraft, or handle key distribution to the military on the COMSEC side.

NSA doesn't do much field intelligence stuff; it's mainly radio/etc. intercepts on military bases, aircraft, ships, etc. Their regular site security is either military or contracted out to Wackenhut or other private security companies, after all (which is apparently what one of Snowden's early jobs was).

The real tough guys of the signals world are the Army's ISA, who do tactical sigint and killing, all in one. I'm sure ISA and NSA cooperate a lot.

http://en.wikipedia.org/wiki/Intelligence_Support_Activity

They're the guys who caught Pablo Escobar. Essentially the most secretive of the tier-1 JSOC units. IMO, the world's most awesome job for a bofh sysadmin -- you get to listen in to enemy communications, and use their improper security procedures to find them, and then punish them (by killing them).

Ubisoft dropped Michael Ironside from the Splinter Cell franchise, so I'm pretty sure NSA has no tough guys left now.

Probably fiction. The NSA might use its black budget to fund tough guys (paying the payroll and overhead), but they'd probably be trained and managed by the CIA and / or military, as part of some joint operation.

It's very common for public officials to get too much money, and not be able to spend it. So they find another agency which wants the money, and organise some kind of joint operation. It keeps their spending nice and robust (so the bean counters don't realise they don't need all that money), and the other side gets the resources they need. It's win-win (for everyone but the taxpayers).