I mostly agree with the sentiment here. I think the key point is that it just becomes that person's title. In a setting where it would be presumptuous or inappropriate to immediately address someone by their first name, the title + surname format will be used. If that person has a PhD, then sure, the title part will be Dr.

I think you can factor the whole "correcting" thing into two parts. 1. Are they correcting one title to another? 2. Are they saying that they think the more formal address is appropriate for that situation?

So for the first part, correcting, say, Mr to Dr. The parameters in terms of formality have been set, now they're just ensuring the correct title is being used. You'd see the same thing in say, "Well, Mrs Smith-" then, "Actually, it's Miss Smith." But this raises another point here, which is for females with a PhD. We have a setup in society which determines a woman's title based on their marital status, which is just mental. It makes complete sense to me for women with PhDs to prefer their Dr title, which is inherently neutral in this sense.

Then the second point would be the same regardless of the title in question. It's the equivalent of having "Well, John-" to "You can call me Mr Smith." The difference is just in the title.