No you don't have to lower it all the way....In fact reversing without the "aid" of the touch or bounce may actually be more difficult and keeps the stress of the weight on the muscles.

I don't go all the way to touch cause I've torn a pec tendon doing so in the past. Albeit I was using a wider grip than I likely should have been with high weights. Either way I actually limit my end ROM on a lot of exercises rather than using my ligaments and tendons to provide some sort of rubber band assist to my lifts.