I've never been taught in medical school to recommend a vegan diet
Medical training recommends diets most patients can stick to, like Mediterranean or DASH. Neither of those is a verdict against vegan eating, and both are built mostly on plants. The major dietetic bodies say a well-planned vegan diet is healthy, and the case for veganism was never only about health.
I'm training to give patients evidence-based advice. The diets I've been taught to recommend first are Mediterranean and DASH, because that is where the clinical evidence and the medical consensus sit. If a vegan diet were clearly better, I would expect it to be the default in medical teaching. It isn't, and that suggests the health case for going fully vegan is weaker than advocates claim.
Not being taught to recommend something is not the same as being taught it is unsafe. Medical schools teach a small number of first-line diets because they are well studied, easy to explain and easy for patients to follow. Mediterranean and DASH fit that brief. That tells you what is convenient as default advice in a clinic. It does not tell you that other diets are worse.
The two diets named also point in the same direction as vegan eating. Both centre vegetables, fruit, pulses, whole grains and nuts, and both cut back on red and processed meat. The disagreement is about the small remaining share of animal products, not about the overall pattern.
On the narrower question of safety, the guidance exists. The Academy of Nutrition and Dietetics and the British Dietetic Association both state that well-planned vegan diets are nutritionally adequate and suitable at every life stage. The one firm requirement is a reliable B12 source, which is easily met. Nutrition also takes up only a few hours of most medical curricula, so what a student has or has not been told is a thin basis for a conclusion either way.
Finally, a health recommendation answers a health question. Veganism is mainly an argument about what is done to animals. Even if a Mediterranean diet were slightly better for a given patient, that would not show that the animals in it needed to be bred and killed. A doctor's default advice does not settle that.
Treating the absence of proof against a claim as proof of it, or the absence of proof for a claim as proof against it.
How it applies here: The speaker treats the absence of any instruction to recommend a vegan diet as if it were evidence that the diet is inferior or not recommendable. Never being told to recommend something is not the same as being told not to.