I didn’t see anything that to me proved the vet actually belittled the owner, rather that the owner interpreted the vet’s lack of a “bedside manner” and “tone” as being belittling when perhaps it could have been due to any number of reasons (compassion fatigue, compartmentalisation, being a more brusque kind of person, being tired etc).
I don’t see any section where the vet actually said anything specifically rude to the owner, rather a lack of specific condolences or offering of special payment plans or “seeming sympathetic” which is all subjective.