... It's not that redheads shed more, it's that because her hair is a different colour it's obviously hers. If it was black-or-brown when wet, and composed of short bits it could have come from anyone or built up from more than one person. Everyone sheds hair, this is a fact. When one has had hair down, there's less shedding in the shower, because it falls out on stuff - on clothes, on the ground, etc., during the day (this is why CSI shows love looking for hairs and checking for the root, because human hair shedding is like pet hair shedding, just we don't sleep on our favourite jumpers the day before we want to wear them). If it's been up, or braided, all that comes out at once. Another time lots comes out at once is when people whose hair likes being washed once-twice a week wash their hair. For wash-every-day people, there's a little bit a day when loose hair comes out, but if one washes once a week, the hair that hasn't fallen out (it was just loose, it was tangled or tied back, etc) all comes out at once. So, if Claire's a wash-once-or-twice-a-week hair type, then yeah.
What I don't understand is why nobody's learned the trick for not getting hair in the drain, or pulled Claire aside and explained it at some point (especially as Claire didn't exactly grow up with female beauty routines being shoved in her face). It's not -that- hard, and there's usually enough that you see it to take with you and put in the trash. I know it's not exceedingly common knowledge, because I had to get my parents to intervene with a landlady on my behalf when she wouldn't rent to me because I had long hair and she was terrified of it clogging the drain, but still, it's something most people who take more than ten seconds and 2-in-1 on washing their hair have at least figured out for themselves. Then again, most QC people have short hair, so...
(In case it's a mystery to people here - when you have hair that's more than about 10cm long, the hairs that shed when you wash it tend to get caught on your hands or stick to you, and you can just stick them on the wall and take the hairball with you when you're done. They don't get near the drain, and all you need is a tiny bit of tile or glass (tile is better) and the water/steam will hold it there until the hair dries. Now, maybe Claire does know this and just forgot to snatch it up because she was distracted, but Faye's reaction makes me suspect this was not the first time.)