Me and my friends all tested this to make sure it was 100% true before I reported it.. When you click F3 to rest or even F2 to surrender, your character will not be able to move, and on occasions not be able to access your gear.
F3 is sit, so I don't know why you'd expect to be able to move...
F1,F2(wave,surrender) I believe this is only due to a lack of animations currently. Rocket stated he wanted to change the wave recently, and I'me sure they'll add walking animations to those later.