Yep, anesthetics today are much more improved. You don't have to be completely under any more, it's basically light sedation, no worries basically. Of course, nothing is risk free, but it's pretty close to it. Depending on the procedure.
Still, we all decide and choose what we'll accept and some tests are not always needed. It happens, but in general there is a reason. Seems like a biopsy is wanted to confirm a condition. You don't have to, but it might make life a little harder if you reject procedures out of fear... I think most of us have that fear factor when it comes to certain things being done.
Only problem I see and I'm not saying you should or shouldn't accept it, but it seems some people just reject a procedure and say I'll live with the consequences. Problem is, sometimes those people have absolutely no clue what or how serious the consequences can be.