I used to live in Eugene a couple of years ago. Spent at least one day a week hammock camping through out the mountains between August and the following May. Never, ever had a problem with unreliable trees. More likely that dead limbs could be a problem than the tree going over. Hammocks in Oregon are a natural because you can camp even on very steep slopes in perfect comfort. You don't have to look for that rare flat spot that is clear of underbrush. So look up and avoid dead branches and bring long tree straps. I found I needed 8 to 12 foot straps in a lot of places. Enjoy the adventure!
"Do what you can, with what you have, where you are."-Theodore Roosevelt