Most of the bags I've seen have the top flap latching onto the (out)side of the bag rather than the top lip. If you turn that around, you'd need to dig between the bag and your body to get to the latch, which would suck.
For a satchel, I have a Crumpler 7M Dollar Home with the flap arrangement; I find that my elbows hold the lid in place just fine while I'm digging through the bag. Problem is that I can load it up so much that it will cause spinal damage, so I've switched to a backpack (Kata 3N1). In theory the backpack swings around for good access but in practise that functionality basically sucks unless you only want to retrieve a 35mm body from the side of the pack.