I was never prevented from shaving. I remember plenty of times, having to shave in front of an upper phaser. They had to see the razor at all times. I think we were only allowed to do it on the weekends though. And probably also depended on the host home.
Since an upper phaser had to watch you, you couldn't shave in the shower. And due to time restraints and the number of girls per host home, it wasn't always possible to take baths. Also, we couldn't request a razor on our wants & needs list. And we weren't allowed to share razors.
So some hostmoms would keep packages of disposable razors for us to use. Same as some hostmoms would keep extra new toothbrushes around, for those times that we got sent to new hosthomes without our stuff.
But the poorer hosthomes wouldn't keep extras. Like for instance Carmen's mom. If you got sent to her place unexpectedly, you were SOL. Hell, her mom didn't even shave herself, so you couldn't expect ANY razors there.