With apologies to Jon and Cool Hand Luke, what we have here is failure to orientate. We're dealing with tensile loads, not shear.
Imagine a rivet looking kind of like a muffin with a top and a
stump.
The published numbers for shear strength are based on loading a rivet in the manner they were intended to be loaded - sideways. It's the amount of force necessary to knock the muffin top off of the stump by pulling sideways on the top while holding the stump in your hand.
The type of failure we're suspecting here is tensile rather than shear. Pulling the muffin top off of the stump by prying it up out of the baking pan after we forgot to put the little paper thing in to keep the batter from baking itself into the pan. Rivets as used in stressed skin construction aren't intended to carry a lot of load in this direction. If you know something is going to be carrying a longitudinal load like a pulley in a control cable, you don't attach the pulley to the bulkhead with rivets, you use machine screws (bolts).
Other than that, Jon's exercise is similar to what I'm pursuing. Figure out the tensile load necessary to pop the head off of one rivet. Figure out how much skin each rivet would be holding in place (by dividing total area by number of rivets). Don't forget to account for the area shielded by the stiffeners (this is problematic if you don't know what the stiffeners were). Figure out what kind of pressure loads your presumed cause of failure (hydraulic, explosive, coconut crabs, etc.) placed on the inside and outside of the structure. Pressure times area equals force. Once you have the amount of force per rivet, compare it to the tensile yield load and see whether your structure is still in one piece or not.
I've attached a stress distribution diagram of how a tensile load resulting from pressure on the skin would resolve itself within the rivet body. The red areas indicate the highest stresses and location of probable failure. If you glue the muffin stump to the counter and lift up on the bottom lip of the top, it will eventually separate right at the junction of stump and top. This is simulated by fixing the end of the shaft and applying a uniform pressure to the underside of the head.