I have heard that some places and areas do it differently, like you have reported. In my experience, F was always 60 and below, 60-69 was a D, 70-79 was a C, etc. "Minuses" would be given for a 60, 70, etc and a plus would be given on a 69, 79, etc. I think this is what is used in our district.

I wonder if systems like you describe are in response to grade inflation.