F stop is nothing more than a ratio between the size of the opening and the focal length.
On the 70-300 f5.6 at a 70mm focal length is a smaller hole than f5.6 at a 300mm focal length.
The opening at the end and the optics of each lens will control how much light gets to the Aperture.
Does that really matter though? The sensor for those two lenses are still receiving the same amount of light.
You can't use a faster shutter speed on a large lens max aperture F/4 than you can on a smaller lens max aperture F/4
Example:
EF 400mm F/4 DO IS USM
This lens has a HUGE opening in the front, its a lot larger than the EF 70-200mm F/4 USM, does this mean it can gather more light? The sensor received the same amount of light when both are wide open at F/4.
Edit: Im refering to what I said earlier:
"If you have a small opening lens with F/4 and 1/500 shutter speed, should have the same exposure as a lens with a huge physical opening with F/4 and 1/500 shutter speed."