FWIW, they made the same claims to me, I believe they all read from same script, sometimes I wonder if I'm speaking with VZW Tech support robots vs. humans who are actually interested in solving my problem. If it makes you feel better, the last tech told me that he gets great speeds on his Galaxy S III in Nebraska. He also went on and on to tell me that VZW has more 4G LTE devices than anyone else (42 he stated), and that it's all of people on the network which is why it's so slow. (Given that my primary complaint with VZW right now is horribly low LTE signal strength all over the place in their "strong" LTE areas, I'm not sure I would blame that on too many people on the network)
Multiple times they have told me "give it some time, LTE is new and we're still rolling it out", but then went on to tell me that my entire area had 4G LTE rolled out at every tower. For a new technology, AT&T seems to be able to make it work properly, which is shocking given all of the problems they had when the first iPhone came out.
I really am at the point where I am wondering if the SW VZW runs on their towers that handles LTE signaling is just broken. It just seems way too hard to believe that VZW just has this poor signal strength almost everywhere when their 3G network is actually better than ATT's in Mass. I realize that LTE is on a different frequency, but you would think 700Mhz would be as good or better than 850 & 1900.