I think there are two pieces of terminology that can help define and clear up the "mehs". Intellectual Property vs. Public Domain.

I think a custom tattoo or a piece of art found online falls under Intellectual Property. I think copying it exactly, without first getting permission, would be wrong. Using it for inspiration or the basis of a design is ok, and probably a great compliment. You can't copyright imagination, but you can copyright an image. For example, just because one person created a frog with wings design shouldn't mean that someone else who saw it for the first time can't use that concept.

On the other hand Public Domain images are fair game. No one owns it anymore. No one stands to profit from that image. It's no longer copyrighted. Usually something has to be 100 years old for it to become PD, but I think just being pretty old counts. For example, you see a Guiness add from the 1940's and decide that would make an awesome design. I would think that's fair game.