I work in a public school and keep my distance from the males as able. There are some men in the school who i have nothing at all to do with and we pass each other several times in a day without even a nod. one day I had to deliver a message to this teacher that his car was parked illegally (sent by the office since I was heading in his direction). Ever since that day he has always nodded or smiled when he passes, says hi or comments on the day.
Do I expect this to start a relationship, ch”v? No, I don’t. But the halachos are not built around me and that particular teacher. What if he was sharing my office and we sat near each other for hours a day and now the silence was broken? This is how people work and denying it is just silly.