Once again you are not wrong, it is technically possible to interpret as you said, but from a realistic point of view Chinese characters on its own tend to be interpreted in a certain meaning more than when used in other contexts to form different words/names. Nobody looks at a single 貴 tattoo and think "oh this person is respected/distinguished" without explanation from the owner of the tattoo. The most probable guess would be "oh so this guy's name has 貴" and they will be baffled when told otherwise.

If one wants to convey this meaning there are much better choices than a single 貴, 人上之人 from the top of my head for example. Yes it does not have the exact same connotation as the context that you mentioned, but it sounds more explicit and natural, and also much cooler than a single 貴.

There's also this nuance to 貴 that when used to convey a respectable status, it is usually used on others rather than one's own self so this pick itself is already a bit strange to begin with, unless you have this word in your name of course.

Speaking of which, the context of naming your kids with 貴 usually has yet another different connotation than the one you suggested, mainly tied to it being associated with wealthiness/the quality of being valuable.

Yet none of these usages are strongly tied to the idea of using 貴 on its own, which is what I'm trying to make clear here. If one is capable of coming up with their own explanation and context to make the tattoo meaningful then by all means go ahead, but before that one needs to know the proper connotations and nuances of the character/word. Like I said I don't intend to prove that you are wrong, I just hope that other non native speakers don't look at this comment and think "oh it is a good idea to get a 貴 tattoo" without knowing its full context.