I would definitely speak to them about it, and would be very upset. I work at a clinic. If we know an emergency is coming in, as soon as they hit the door we're ready to take the pet to the back and start treatment. Some times owners don't realize the dire situation their pets are in and underplay it so we aren't going in thinking "this animal needs urgent care or it will die", but our receptionist staff does a really good job at giving us a heads up if an animal comes in and is extremely ill. It doesn't matter if the vet or techs are in another appointment - if an animal needs immediate attention, that animal will get immediate attention.