According to what I have read, Winchester decided on the .277" bullet as a proprietary 7mm cartridge. .277" is exactly 7 mm. Perhaps they didn't want any other 7mm rifles rechambered to their new cartridge, since the 270 Win is very close to the 7X64 Brenneke, which was quite popular in the Mauser rifles being imported between WW1 and WW2. There were a LOT of proprietary calibers during that period, like the 40-60 Winchester and 40-60 Remington, which were totally different cartridges with different diameter bullets. The list of reasons goes on and on.
But Winchester's choice of the .277" bullet did lead to some very creative writing wars between Jack O'Connor and Warren Page, both well-known writers from the 1930s until the early 60's. O'Connor was billing the 270 Win as the only cartridge to shoot anywhere for any reason, and Page was a supporter of the 280 Remington for any animal short of Cape Buffalo or elephant.
Interesting side note- the only other rifle in the world to have ever used a .277" bullet was the pre-war Chinese service rifle.