Surely the enjoyment they provided was that counts: why stress out over "authenticity."
(Banksy comes to mind for some reason: he vandalises property over various causes and no one questions his authenticity. Does anyone think he's suffered like the caricatures he depicts?)
I still believe they are undiminished as books and enjoy them from time to time.
Some things hit harder when you know stuff from his real life, for example those stories about depressed people (I remember the story of the young man who takes his own life when his dog dies, and how cheerful he seemed) and then I read the real Herriot suffered from depression. So I guess he was somewhat writing about himself?
Also, somewhat contradicting what I said above, the stories might be fictional but they ring true of the English countryside and the farmers of the transitional time Herriot describes. That the stories aren't literally true doesn't detract from that. It's a bit like what American author Tim O'Brien explores in his writings, that verosimilitude can be as important, if not more, than actual truth.
I have seen statistics which state that vets more likely to commit suicide than GPs.
And the story about the young man and his dog rings true. A close friend always breaks up when he remembers how he had to put down his dog due to cancer.