.30-03 was still being loaded by Winchester, Western, and Peters in 1925 when the .270 was introduced. Remington may also have been loading the round. It was still being commonly used by shooters.
Winchester's designers were not adverse to using older rounds as the basis for new cartridges. Another prime example? The .220 Swift, whose parent case was the 6mm Lee Navy, which was designed around the same time.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.