I feel for you in your fence line dispute. Sounds like you've gotten some good advice about legal issues, so I won't add to that.
As far as surveying goes, let me the perspective with you of someone who's done a lot of surveying. First, "his buddy with a GPS" is pure nonsense. He's trying to spew some technical sounding terms to try to scare you off, and make himself feel smug. Hand held units are only accurate to within 15 feet or so, which is useless. Besides, unless he pulls maps and somehow figures out the exact latitude and longitude, his hand held unit isn't going to be any use.
He sounds like a bully -- I'd ignore his blatherings. You did the right thing in getting a licensed surveyor to check your line. The only thing that will hold up in court is to have an actual surveyor put in monuments on your line. It's not much of a crime, but in California where I learned to survey, it's against the law to pull out monuments, since they're legal limits.
As far as GPS surveying goes -- it's a huge part of the surveying industry, and getting more common all the time. 5 years ago, when I started using it, the base station for a differential system was a small transmitter mounted on a tripod -- about 5 feet off the ground. This was put over a known put, often a state benchmark. From this base station you have a 6 mile radius to work within. The portable unit mounts on a rangepole, is quite small, and weighs no more than 10 pounds altogether. Accuracy used to be on the order of a tenth by a tenth (tenth of a foot). Sometimes it was as good as a couple of hundredths of a foot, depending on satellite coverage, which is just as good as conventional surveying. If the coverage wasn't good, the accuracy dropped quite a bit. Under tree cover and in mountainous country, conventional surveying is still necessary.
I've gotten out of surveying the last couple of years, but I understand that there are more satellites available now, allowing for even better accuracy.