Forget the general consensus!
Why?
Because it is mostly coming from people who have no personal experience with applying with a significant amount of undergrad online work and successfully treading the medical school application process.
It has been done in the past (which I can personally testify to), and I suspect it can also be done in the present (and future). Not all schools will be online non-trad friendly, but many (if not the majority) will. One's best bet is to schedule a personal (or phone) meeting with a person in the school (not secretary) involved in admission decisions, and present your case to them - take it from there.
Just like for traditional brick/mortal schools, there are many factors that will make or break one's application. The school you attend, the grades, your LORs your extracurricular activities, "MCAT", et cetera, et cetera...Fax mentis incendium gloria cultum, et cetera, et cetera...Memo bis punitor delicatum.
And OP, to answer your question, Law2Doc, in my opinion gave you the best advice. If she/he (professor) does want to give you the letter, make sure it's a strong one that highlights as many of your positives as possible. If she/he (professor) teaches in a graduate program, it would serve you well if she/he states [in the letter] she/he would be more than glad to have you at her/his program should you not wish to pursue a medical education.
Let me know if you need more help. 🙂