I've been to 46 and have lived in 11. I count it if I have gone through immigration and spent some time there. I haven't counted things like driving up to the Syria/Irag border and sticking my toe in Iraq, technically I was there, but I don't count it.
For the purpose of conversation I think the OP's idea of walking through immigration and getting the stamp should count, but with an * next to the country name in the fashion of a steroid achieved sports record.