When I was a CFO/CIO (several decades ago) the big box vendor NEVER refused, they simply said 'next or after next release' or the price to do it was BIGBIG bucks! They essentially wore yo down or priced you out.
The reality is no vendor is stupid enough to just say NO!
I don't work for a provider so could not vote, but once worked for a small vendor whose system was wanted by a group of clinics that were on a large health system's instance of Epic, and the health system, not Epic, refused the integration request from its clinic customer.
We use Epic and they have never refused a request. We don't make that many, but they've never refused.