The 270 Winchester cartridge as we know it was invented by the Winchester Repeating Arms Company back in 1923 and released in their Model 54 rifle in 1925.
Who knows if anyone had developed a cartridge based on the .277" bore size before that. Would seem strange that an arms company would come up with what is an 'odd' calibre although they may have decided to invent something between the 6.5mm and 7mm just to have a marketing difference.