I think what people fail to realize is that by actively singling out black people as needing the attention to not be singled out, and then changing a nursery rhyme, they're actually being more racist than they'd be if they left well enough alone. Think about it, if a bunch of white people change a nursery rhyme to avoid "offending" black people, then they assume that black people would even be offended in the first place, and therefore feel some need to protect them from this supposed racism, by using a different type of racism to do it.
If they truly wanted to avoid any sort of racial inequality, they'd just treat everybody equally and ignore race altogether. Totally ignore it, too. As in, not even acknowledge if you're black, white, red, yellow, or any other shorthand racial colour I'm forgetting. "So you're black, who cares?" "So you're white, who cares?"
Funnily enough, I keep getting told that that particular ideal is racist in and of itself, which is ludicrous when you realize that only if you totally ignore race altogether are you not singling out any one race over the other and therefore aren't being racist.