I used to get sore shoulders after a day of pins (although it wouldn't seem painful during the pin itself). I found doing a few simple exercises to strengthen the muscles around my shoulders got rid of that problem.
Personally I find basic fitness really helps with ukemi. The muscles around a joint apparently play a role in protecting that joint.
It's more than that: the muscles surrounding a joint are primarily what hold the joint together when it comes to putting serious athletic stresses on it. If you try to lift, throw, or pull something and your muscles are so relaxed that nothing but ligaments are holding the joint together, you are in trouble. This is also why excessive passive stretching is not a good idea.
Moreover, strength exercises not only protect the joint by strengthening the muscles that stabilize a joint. So long as the exercises involve actually handling weight, as opposed to using a machine, strength exercise strengthens many of the tissues involved in the joint themselves: bones, ligaments, tendons. Proper strength exercises also provide a way to help learn and ingrain healthy movement patterns - like squatting, lunging, picking up something heavy - and assure that your body is well used to doing such movements when they come up in more stressful and less ideal situations.