The pavise was usually held by someone else, so he could always vary the angle at which it was held. Another thing is that arrows and quarrels are noticably slower than bullets (you can even see musket balls in flight), so the crossbowmen should have been able to see the incoming volley and take cover at the right time, especially if said missile duel took place at long range. No laser sniper rifles in 1415, sorry.
Maybe it's a case of bad documentries again. but all the pasives i've seen where bassicly just big sheilds, if the arrows where coming in mostly vertical their wouldn' be anything to take cover under if you kept the passive vertical, and if you tipped it horizontal you'd have to be crouched which would prevent you reloading the Crossbow in all probability. (Arkward position and all that.