bigbamaguy - with thick-barked trees there's probably not a problem...but imagine thin spectra (which is pretty hard and doesn't flatten out to distribute the force) wrapped around an Aspen. The pressure on a hammock would likely (IMO) cause damage to the part that was under force...probably 1/2 to 3/4 of its circumference. That's enough reason to use straps, IMO.
I think that as long as SOMETHING is distributing the force from the cord, it can serve the purpose. Youngblood often uses (or used to use) hollow rope that flattens out to distribute the force. That may work just as well as webbing. Other folks seeing it may not make the connection, so perceptions are still important, though.
I think the tarps are different. I don't put anywhere near the force on my tarp that I do on an occupied hammock. But if there's enough force that you're risking damaging the tree, then surely something should be used to protect it. Straps would work.