She responded by that she doesn't use Interfolio and that she will upload the letter when a school asks her for it.
Clarifying question: did you get a hint of animosity when she said this to you? Dossier services have been considered best practice for graduate school admissions at least since I first started college in 2013... it would be bizarre that she wouldn't be familiar with this if she has presumably written for other students in the past.
The way you phrased it makes me wonder if she has had experiences with her letters being manipulated in some way. The other aspect that comes to mind is that she is planning on writing an outwardly negative or "fair and balanced" evaluation (which functionally, is the same thing) and she doesn't want you to know that she would do that. (I am getting the vibe that, in other words, she is trying to enforce—irrationally—that you have waived your right to see the letter).
My two cents, which someone out there will inevitably disagree with, is that the entire procedure, from asking a professor for an LOR to having the letter delivered, should be a very positive and encouraging process.
Just my opinion, but if you're not hearing some degree of some derivative of: "Oh my goodness, I can't believe you're at this point! Congratulations! I would be so pleased to write you a letter and support you through this next season of your life!" ...I would have reservations about pushing them to write, or using that letter if they already have.
I think, to get to the point where LORs matter (i.e., you got to the point of interviewing and you're being considered holistically), a lot of things have to go right. And to be shot down over a negative or lukewarm LOR is a fate so demoralizing I genuinely cannot even imagine occupying that emotional space. I would also consider such a behavior on the part of a professor to be unprofessional, considering what one has to do to apply to medical school these days.
I'm aware that everyone has different personalities and people are entitled to having a bad day, which is why I ask whether this was a pattern, a one-off, or something else.