Yes military working dogs are the best. This much is certainly true - most of those that live in the middle east are PETRIFIED of military dogs. I assume it has something to do with the fact that as Muslims they don't like dogs. The dogs they do have they treat like crap (why they keep them around the house I'm not sure - I suppose it's like an alarm system because they bark at everyone). As I would walk around the Iraqi villages, the dogs that were hanging around people's houses would bark at everyone that wasn't in the family. When we would stop to talk to them, the Iraqis would then throw rocks at the dogs until they were quiet or ran a little bit away.
As to the video - I had never seen or heard of someone jumping (in the Airborne sense) with a dog - that's cool! I wonder what the dog thinks. For as much as they like to stick their heads out of cars, they might like it!
They show Cpl Dustin Jerome Lee at one point. He was actually assigned to the Marine Corps Logistics Base in Albany where I am stationed. In a cermemony last year, they dedicated the kennels here on base the "Cpl Dustin J. Lee Kennels". Here is a Wikipedia page on his dog.
Taken while in Iraq. Marine K9 Lex with Cpl Dustin J. Lee