Exactly! And in order to elevate the amniotic fluid to an unsafe level (i.e., to raise the mother's core body temperature), the bath water has to be so hot that it would scald the skin.
There are a few other things in that book that weren't quite right...so if you've got any doubts (like about training), ask your doctor.
The general rule is that you can pretty much keep doing anything you're already conditioned for, as long as your body doesn't send signals that it doesn't like it. One thing you might have to change (in addition to eliminating squats) is how you work your abdominals. Past a certain point, laying on your back can cut off blood flow to the uterus, so you can work your abs by getting on all fours and using them to lift that belly! (And pelvic tilts work great, btw, when the baby is resting awkwardly and giving you discomfort in your back.)
And don't forget to do your kegels! I did them religiously for my first, but didn't for my second...and it made a HUGE difference during the delivery.