Recommendation letter submitted by applicant in application Problem

In one of the research internship programs I am applying for in Japan, the institution requires me to directly upload recommendation and, otherwise the application will not be reviewed. However, I think this is not quite appropriate since generally applicants should not know the contents of the recommendation. I contacted the admission administrators to discuss other options but they said it was that institution's policy.

Now I am wondering if I could ask for the professor's recommendation. Even though I think he will understand the situation and there are examples that the professor voluntarily send students a copy of recommendation (i.e. the students receive the letter passively), I feel actively asking for the copy truly unprofessional and may make myself look bad in professor's eyes. This matters since he will provide recommendations to other institutions, where they follow the convention and accept recommendation through direct email with the professor.

Do anyone else have similar experiences and how do you do with that? Thank you in advance.
Instead of asking the professor to give you the letter, tell him about your predicament. Mention that you checked with the internship program and were refused any alternative, and ask for advice. Be clear that you completely understand if the professor is not comfortable sharing the letter with you, and consequently would be unable to help you with this particular application.

If the professor is fine with you seeing the letter, he may offer it anyway. Even if he is not, it should not look bad on you, since you were left with no choice and were just trying to work around the program's requirement.