Your post was quoted in a BBC News article today...
The quote they selected was this:
Checking your privilege doesn't mean anyone is asking you to say "I only have things because I am part of privileged groups". It does mean someone is asking you to say "By position of a characteristic I was born with, I have been helped, or at least not hurt, more than others without this characteristic". It does not mean anyone wants you to apologize for it; it does mean someone is asking for an acknowledgement of the implications of it, either for how it is impacted where you are now, how it might be skewing your perspective or level of knowledge in discussing a subject, or for how the lack of that same privilege may have made things different for someone else.
ETA: Your original post was spot-on.