Absolutely. I'm sure they get a lot of support requests that end up client software related, and given the variety of sites they deal with, it would be a mammoth task to be able to diagnose these all the time correctly. So they default to the 'it's your code' answer unless they have clear evidence to the contrary.
Your best bet is to do your homework and provide as much specific data about the scenario as well as a way to reproduce it when you contact them.
In this case, the error logs and an internal Apache error message was the clue. No client code problem can cause internal Apache error messages. If you have that evidence on hand, it's on them.