I am a professional piercer. I always use 316lbm stainless steel and internally threaded jewelry. Externally threaded jewelry actually causes rips and tears in the tissue when inserted. Not knowing what grade jewelry they gave you, I am gonna hope what you have is fine and that they were just trying to get more $ out of you.
This I think is the case, my son had a piercing in his tongue, and had to have it redone because it didn't heal right. I had mine done the old fashioned way, used to ice cubes, got numb, put thread on a needle, and ran the needle through to pierce the potato. Cleaned the string 2 times a day, and moved it around.
I think it depends on the person. I am extremely sensitive to certain metals so have to make sure that any jewelry I wear at all (whether thru a piercing or not) is a higher quality. I can tell within about 10 minutes if there is a problem since I start to break out in a rash. My 24 year old daughter has tried to get pierced several times and no matter what they use, she ends up with it getting infected. So I think it really comes to down to your body's reaction and healing.
Yes, as the matter of fact jewelry can affect healing in initial piercings.