The only thing I've done to me in the biz is cut slice my knuckle ...
Well, since you are doing a full confession, I will reciprocate.
I have buried one climber. This was a full fledged, on the job fatality. Another time, one of my lawn workers grabbed the wrong chainsaw (no safety brake, and I told him to take the 009!), and damn near cut his face in two pieces trimming weed trees out of a chainlink fence.
That was expensive. Apart from that, we have had about 30 stitches from chainsaw cuts in the last 25 years. Myself, apart from a couple of broken ribs incidents, I have never gotten more than a scratch doing tree work
Liability claims: none, except for an $80,000 damage claim for cutting some underbrush off a lady's yard in exchange for using her property to access a billboard. She denied ever talking to us.
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By the way: if you think it's always a close call, you are doing it wrong. Done right, tree work should mostly be safe when done carefully and properly.
Today, we dropped two 85' Ailanthus trees into a 28' wide drop zone. It wasn't close, it was easy. We took our time, trimmed the wide branches off, gunned the sights on our face cut carefully, and dropped them in. I did the first, dead center, with at least 8 feet on either side. My climber was a bit off to the side, but he still missed the parked truck while I stood at the end of the drop zone and enjoyed the breeze. I knew exactly where it would fall, and I was at least 15' beyond. It wasn't close, I was just catching the only breeze on a hot day.
You should be living to enjoy the mastery of your trade, not the adventures caused by any lack of skill thereof.