I read some of the comments. What is a 'black redatart', I though it was a black redstart. Nit picking perhaps, but two contributors spelt it that way. Also, what is a 'hangman's jam knot'? Frightening, I think.
Well accidents will happen and line will get tangled in trees no matter how careful you are. The thing to do is minimise the chances by choosing your swims carefully, look before casting, and attend work parties to clear any threatening branches.
Saying that, just last week I made a cast with a plug to just one side of a tree. The plug landed where I wanted, but the stray line blew over a branch. Try as I might that plug lifted into the twigs and only because I was on 30lb braid did the twigs give way and I got my plug back.
It can happen to the best of anglers.