Ginko:
Hate to admit it, you just described my situation exactly. Finishing up a medium sized silver maple back in 2006. Just a few limbs near the gutter to go. Too big to let fall on the gutter, but not big enough to rope. From the bucket, I grabbed the limb with my right hand, started to cut with left hand. The saw wasn't sharp, and the branch sloped down toward my right hand. Saw skipped when it touched wood, and got my right thumb. Didn't hurt immediately, but I knew it was bad.
Cut to the bone and severed my EPL- the tendon that's visible when you place your palm flat on a desk and raise just your thumb. They actually had to make another incision in my wrist to find the tendon (which had retracted up my arm) to fish it back down and sew it back together. As I think about it, it kinda sucked.
Six weeks off, physical therapy, etc. Thumb still doesn't work like it should, but I'm lucky it works well enough.
Point is, it can and does happen. No excuses from me. But most who run buckets have made thousands of cuts. We know the risks, and we know how to avoid them. Sometimes we get stupid, cocky, lazy, tired, whatever. Human nature. I know this much: complacency will come to collect. (Especially if your saw is dull.)