How could he possibly know that? The tattoo is NOT of a battered woman much less Rihanna. Why would he even care if people DID make a connection (which doesn't exist)? It's his life and he can do whatever he wants no matter what the tabloids write about him.
Here's the thing, I imagine that if he was questioned about the tattoo, in an interview for instance, his defense would sound pretty similar to what you said. Something along the lines of, "That's not what this tattoo is about, and I don't care if people think that, because it's not true, so who cares what they say."
The reality is that it's pretty easy to see that tattoo as a battered woman, whether or not that's what it's supposed to be. A good percentage of the people who see it will think that that's what it is. Given his past, it would have been in better taste to ultimately decide not to get the tattoo. You're right: it is his life, but when the average person even hears the name Chris Brown, they connect it with two things...his music, and him beating up a woman. As a celebrity, he would do well to consider how his actions will affect his public image.