A hennessey hammock is not 'obviously harmful' to trees. The hennessey attaches to trees by wrapping an inch-wide nylon strap around the tree and attaching the spectra hammock line to the strap. The strap spreads the force of the hammock over a large area of bark and does not hurt the tree. There's probably some trees with thin bark that can be damaged, but generally it should not be a problem.

Of course, a park ranger may not know, or care, about the distinction between a strap hung hammock and one that uses just a rope. The park may have a policy that does not distinguish so even if the ranger knows you are not damaging a tree, you may not be permitted to use a hammock. Campgrounds are high impact zones, so care must be taken to protect the area.