Well for ground work I would agree but I expected to be way past ground work and have a rideable horse in 4 months so I wanted someone who knew how to ride a gaited horse.
We've got two issues going, here.
First is your difficulty with Ms. Graves. I've met Liz a number of times over the years and this story disturbs me as it seems very out of character with her.
The second issue is the more general question of the necessity of a "gaited horse trainer."
As far as riding is concerned, even basic under saddle work does not vary much between a trotter and a gaited horse. There are more complexities with getting a specific gait than there are getting a generic trot, but when a horse first goes under saddle the wise trainer looks for a quiet, forward, horse yielding to the bit more than any sort of specific gait. If you get that gait, then God Bless You. If you don't, it's not a concern at that time
I would agree with you that if you sent an unbacked horse to a trainer, any trainer, and it came back unbacked after 120 days then there could be a problem. But I would have to ask "what were the terms and conditions of the contract?" If you did not contract to have an unbroke horse ridden then it's no surprise that it was not ridden. I'm not privy to the terms of your agreement so I can't make any specific comments. My general comments, however, I think reflect the standards of the industry.
Anytime anybody engages a trainer there should be a clear writing setting out what the trainer is to accomplish, how long they have to do it, and how much it will cost. This need not be a multipage document on legal sized paper; it can, literally, be done on the back of an envelope. But it should be done so that each party knows their respective responsibilities.