He's wrong but it's complicated. Here’s a short article on the subject: https://www.formsofaddress.info/doctorate/
As the author explains, context matters. If Jill Biden were teaching a college class in education or giving a speech on the subject, her expertise would be relevant, and it would be entirely appropriate for her and others to refer to her as Dr. Biden. In a purely social situation, not so much. In fact, it would probably be considered pompous and a bit naïve of her to use her academic title then.
The same holds true with other non-medical doctorates, such as Ph.D., D.M.A., D.B.A., D.Eng. and the like. However, those with medical degrees are treated a bit differently, at least here in the United States. In pretty much any situation, professional or social, it is appropriate to use the medical doctor’s title. In other countries, all bets are off. Local custom prevails.
Finally, the legal profession here has long considered it inappropriate for lawyers to call themselves doctors, even though they hold juris doctor (J.D.) degrees. In the old days, it was to avoid the appearance of “self-laudation,” or self-praise, and had more to do with ethics than anything else. But today it’s to avoid confusing the public, who tend, as did the TV commentator, to associate doctors with medicine.
I found what I consider to be a safe middle ground. I never refer to myself as Dr. Lamb but, since I do use my advanced training in my work, I sign professional correspondence with "Ph.D." following my name. I earned it and I'm proud of it. 'Nuff said.
Rick Lamb, Ph.D.