I am somewhat surprised that the transplant team would offer such an organ, but then again "beggars can't be choosers."
Sure they can. My MD told me he advised one of his patients to decline a kigh KDPI kidney, and she got a lower scoring one a few months later.
Many "high risk" kidneys come from risk populations, not known infectees. Nucleic acid testing has reduced the time from HIV infection to detectability down from weeks or months to days. A transplant surgeon told me that his center transplants these high risk kidneys (generally street people, drug users, etc.) and has never seen a HIV infection.
Although I do not subscribe to the clinic director's philosopy of "Don't worry, Hep C can be cured now (....if you can pay for the $95K Rx) and HIV can be managed". My neph's reaction to the later part of that sentence was "No, you really don't want to manage HIV".