I thought the 6.5 is supposed to be .257". I recall someone correcting me on that a year or 2 ago, when I (mistakenly, or was it?) mentioned that .264" was 6.5mm, just as you did.
Using window's calculator, .277 (aka the 270) converts to OVER 7mm. But since the "official" 7mm designation (.284") is actually 7.21mm, if you take away approximately .2mm from that, it DOES actually come out to 6.8mm for .277cal, even though THAT conversion is likewise, not a "true" one.
Could it be that the entire range from .257" through .264" is considered 6.5mm, and the person who originally "corrected" me didn't know that, and hence "wrongly" corrected me?