The point of the hand stamp is make sure you didn't get your ticket from someone else who used it earlier that day. To enforce the nontransferable rule. So when they scan you ticket, it will show you already came earlier that day or that you park hopped, and if you don't have your hand stamped then they might think you got the ticket from someone else. Does that make sense?
Earlier this year, DBF and I were in line to get our APs scanned and there was a group of 3 people in front of us. The CM scanned the lady's ticket and asked to see her hand stamp, and she didn't have one. The CM looked around for another CM and couldn't find one, so she scanned the tickets of the other people in her party and they all had hand stamps, so the CM let the lady go. She really shouldn't have, but I think the CM didn't want to go find a lead to ask if they should let her go.
No, you don't need a hand stamp if you have an AP since your picture comes up. I get one anyways though!