Not necessarily. Remember that video where Chris is yelling at the MALE JERK in the Shovel Mech? She doesn't stutter once. Her voice is improving and she could probably ask for the piercing and sign the waiver without bringing up blue arms or something. And it's not really fair to assume that Chris is not viable for a piercing just because of appearance; she could be a completely sane and reasonable trans woman who happens to not be very good at passing, or might not even be trying to pass on that particular day. It could be considered discrimination to refuse Chris the right to get a piercing based solely on appearance or mannerisms if she didn't say or do anything of concern.
On the other hand, it's very shady that the piercer would do it a second time even after seeing the wound from the first time. Most of these places won't even give you a piercing if it even looks like it might reject or cause damage (my friend wasn't allowed a wrist surface piercing because she was slightly too skinny for the jewellery to fit comfortably and it had a higher chance of rejection because of that), so it's very worrying that the piercer would look at Chris's existing infection and think "hm, yeah, well dat looks okay"
Did you really need to throw in that thing about pus?