I was thinking about this again last night and something occurred to me. I worked a number of years in a doctors' office and very often, for established and new patients, what should and would have been considered urgent medical situations by the healthcare provider often were not considered as such by the person(s) handling the phones. If the caller didn't speak directly with a provider, or the phone person did not convey the message properly to the provider, a patient's situation could have been mishandled. Speaking for myself, certain things (chest pain, breathing problems, bleeding, etc) always set off the alarm to me - better safe than sorry - but not every person answering the phone interprets caller's words the same way or has enough medical knowledge to hear the ding-ding-ding.
The phone operators are very rarely medical professionals, at any office, and you have to be adamant about getting your message to the provider. If, of course, you spoke directly with the vet and were still blown off, then yeah, I'd definitely be ticked off. Regardless of whether the schedule was packed, if unable to squeeze you in they should have at least offered to refer you. It's not like you were calling because your dog had the sniffles.
I understand about the food, though. As another poster mentioned, there are legal barriers preventing physicians from issuing prescriptions to patients they have never evaluated, and most healthcare providers will not issue prescriptions to patients that have either not been seen for a long time, or for conditions that have not been evaluated in person. If the food is Rx-only, well... seems silly but it probably comes down to legal concerns.