Had exactly the same feeling. I felt bad for the GH employee who responded. He was helpful and thoughtful, made it clear what the problem was, offered advice and promised to make whatever's possible on their end...
...only to have someone come up and act like a paying customer whose expectations weren't being met. He answered suggestions by saying something that comes down to "I don't understand, can you repeat please", and never quite grasped that if he wants a better experience for his users, he also needs to work for it.
The introduction to the response, in typical douche manager style, was the cherry on top.
Even if they were a paying customer- what would you do if GH could support that volume? Obviously there are SLAs in place if you're big enough, but at the end of the day, if they simply just can't handle the volume what are going to do? 'Nothing' isn't the answer if you want to maintain users. You'll have to solve the problem no matter what, it just seems really egregious to me to have that response when you're not giving anything back (money or time) to the team that is essential allowing your service to exist.
And it had this passive agressive ring to it, with the hand clapping and the hurray in the beginning and the stone walling in effect.