I didn't explain very well.
The fencing company is already in the garden talking to the client.
They're pricing a fence, either a tree(s) is in the way and they offer to remove it or as a garden service the client says "do you do trees as well? as I want this one out"
It's not really much of a leap.
As for climbers, yes, in the U.K. At least, they're a dime a dozen, $175 will get you a passable climber for a day.
Insurance? Well for a start you go without, as things progress you can get some.