Makes a lot of sense actually, but I have heard that the tattoos themselves are thought of as "unclean" in a way that the bath cannot clean. Makes me think of, back in the early 90s, we were so afraid to use a drinking fountain, like in public, after someone who was infected with HIV had used it. You know, the big AIDS scare. We didn't know it couldn't be transmitted that way. I always felt like the tattoo taboo in Japan had similar energy.

correct, and from what I've heard often much less of a problem if you're clearly a foreigner.

if you're covered in tats you might run into some trouble but I've talked to some people with pretty obvious tattoos who said they were allowed in the majority of onsens they tried.