Yeah. I realise that my dog is both a blessing in that she gives me legitimacy for being where I am, can be a distraction, and gives me valid reasons for keeping my distance if I so choose; but could also be my undoing if she is recognised and so draws attention to me.
Fortunately though she is a common breed around these parts. I also think that she diverts attention away from me for the very reason you mentioned. Same thing applies to joggers. I now completely disregard both joggers and cyclists as they are more preoccupied with what they are doing (including keeping an eye on the dog!) and don’t have much time to study every girl they pass by.