They brush their hair in the bath should be accepted too. baño means bath its use as bathroom is an abreviation of cuatro de baño, room of the bath
I wonder. That's what I wrote, and kicked myself - I mean, it would be a strange habit and it would block the drains! Also, the Collins dictionary says the bath (tub) is 'el bañero'.
"La bañera" is the bath tub, but not "el bañero". But baño can be used as a term for all of "bathroom", "bath tub", or "toilet room".
The reflexive form "se cepillan" is used here, so they're doing it to themselves. If they were to brush "his hair", you'd use "le cepillan" here.
Lav was accepted, but not bath?
In the US the only time I ever hear the word "lavatory" is on airplanes. I guess they want to make sure we understand there is no actual bath in those tiny little outhouses they have on planes.