I don't think that it "isn't allowed" but a resident (especially a PGY-2) hasn't led residents and medical students. Residencies are set up differently but they are all pretty much based on progressive autonomy and leadership. So I know a 3rd year of any specialty has led more residents and medical students, and seen more, than a first year. And an attending has made it through residency where they were in their final year responsible for many patients and residents as well as developing the sense of autonomy and awareness to help guide others in the correct way.
PGY2s don't know squat in the grand scheme of things and that is why residencies are at least 3 years. A PGY2 in surgery is basically a beginner. With the exception of a chief resident, I would personally blow off a LOR from a resident.
I don't think a PGY2 letter is going to be much help. Beside if you are shadowing a surgery resident, how are you not interacting with the surgery faculty enough to ask them for a letter? As a general surgery resident my students and I are always with faculty in clinic and OR. Usually if you worked really closely with a particular resident they can give some specific input to the faculty. Also my chiefs dont write letters either, they usually just give input to the faculty.
Now if you mean that this particular resident is the only DO in the program, well IDK what the point of the letter would be. I am not a DO but when I did apply to DO schools, my understanding was that a DO letter was supposed to show that you have experienced some osteopathic principles. If this is a DO TRAINEE in an ACGME program in a field is historically anti-DO, I agree with FrkyBgStok (I would blow off the LOR).
I applied with an MD letter only. A handful of DO schools specify it had to be DO. If you have low stats this is more important to get. I understand it’s been difficult, and maybe DO schools will be more lenient about that? Though I don’t know for sure, but a lot of other concessions being made due to the pandemic.