No, everything you say is right.  As a broad and general principle it's best to acknowledge people's common humanity before one addresses the peculiarities of the shell they live in.

Going to try and find the original comment about this, but Facebook search is shit so it may take some time...

My humanity is anything but common, dahling!

Although, strangely, if you're a policeman (or policewoman, let's not be sexist about this), it's the first thing that gets mentioned when you're being introduced to someone. No one ever thinks about how that feels. You bastards.

It's just a heads up - kind of like when you take a call from your best mate while on hands free with your wife in the car. "Hi mate, how you doing - you're on hands free, say hello honey"

two of my sister's close friends are tax inspectors, that gets mentioned quite early in their introductions for the same reasons (so people don't accidentally incriminate themselves)