A valid point, I'll give you that. However, allow me to explain.
The earliest influential time the Doctor visited Sol III was approximately 100,000 BC (An Unearthly Child). We'll skip the fact that the cavemen had totally developed language. But, naturally, they didn't have a doctor. Thus, they didn't have a word.
The Doctor's native language is likely Old High Gallifreyan, but the common language was Circular. Now then, let's just pretend for a moment that the Doctor, when he went off by himself to collect plant samples, and happened to mutter vɛnɪç. The Tardis can't translate this for the cavemen because they have no equal for it to be rendered. (And because the Tardis doesn't translate Gallifreyan.) The Doctor helps heal the injured caveman (forget what his name was-Zog, I think) and so they associate the two.
The oldest language from which every language in the world derives in Proto-Indo-European. You can check out the full web here
. From what researchers can discern, the word for doctor and similar words was "médodiks".
Vɛnɪç --> médodiks
How? Well, mɛdodɪç. A little confusion, lost in translation. (And "dodag" is Gallifreyan for person. *wink wink*)
Proto-Indo-European slowly passes away as people spread out in the world and develop new words for new concepts and just evolve the language on their own.
Now then, on the one hand, we have Indo-Iranian that will eventually become Persian, Kurdish, and Sanskrit. A remarkable number of words come from Sanskrit. Unfortunately, doctor is not one of them. However, the Sanskrit word for doctor is "vaidya". Again, a little confusion down the language tree, but remarkable similarities, wouldn't you say?
Vɛnɪç --> médodiks --> vaidya
On the other hand, we have Italic languages, which will eventually give rise to Latin and her child languages.
In old days, doctors and teachers were basically one and the same. Some also had duties in the Church and thus derives a whole new set of words which we are not concerned with. So, Latin, has docere (later: decent) and doctor. But this doctor actually meant teacher, advisor, or scholar.
Doctor later became Old French doctour. Doctor of medicine did not come around in common use until much later when it was combined with medicus or medicina. Also in use was physica.
--> ??? --> vaidya
Vɛnɪç --> médodiks --> medicus --> doctor medicus --> doctour --> doctor of phesike --> doctor
-> miege --> médicine --> médecin --> medicine
The third line is the evolution of medicine from Latin to French and then English.
vɛnɪç --> mɛdodɪç --> mɛdɪç/mɛdɪkuç --> mɛjdʒ --> mɛdɪçis --> mɛdɪçɪn --> mɛdɪsɪn
So, as we can see, vɛnɪç actually later became "medicine" but the understanding and attribution became "Doctor".