The lack of an agreed-upon, objective definition of racism is a problem. People are coming to realise that it's much more than just overt, KKK-style racial hatred, and can manifest itself in much more minor ways.
But still, it's unrealistic to say that anything a Black person perceives as racist is therefore racist. Black people are going to be wrong too, sometimes! (Of course, referring to your last paragraph, that still wouldn't mean that what the Black person experienced wasn't *real*, or really *felt* by them; just that their characterisation of it might be mistaken.)
I honestly don't know what the solution is, but I do know that the whole discussion about race is muddied by a lack of clarity in terminology.