Not contrary at all, this is how useful discussions are had!
Ok, a lens has a focal length. A lens has an aperture. Both of those intrinsic values are independent of sensor size, indeed they are true even if the lens is not mounted to a camera, like binoculars or a spotting scope.
If we are going to start throwing 'equivalents' out there then one, why, and two, shouldn't we be all inclusive, why just arbitrarily pick focal length?
It is true that on a 1D MkIV a 300mm + 2xTC lens gives you the field of view of a 780mm lens on a ff camera, but it doesn't give you the subject magnification of a 780mm lens on a ff camera, nor the dof. It gives you the subject magnification of a 300mm + 2xTC on a FF camera. Few people ever point out the 300mm f2.8 + 2xTC on a 1.3 crop is equivalent to a 780mm f8, why not? Because it isn't relevant, who cares what the equivalent is unless you want to take the same shot from the same place with a different sized sensor. A 300mm f2.8 on a FF camera is exactly the same as a 300mm f2.8 on a crop camera, it is a 300mm f2.8.
Now you ask about shutter speed, and that is a good point. Why, if a 300mm lens is just a 300mm lens on ff or crop would I need to use a faster shutter speed on the crop camera? Because of enlargement, the CoC for a crop camera is smaller because the output size is taken as a constant, if the CoC is smaller then any movement will be enlarged more, hence the need to use a faster shutterspeed. To be sure, if you take two pictures of a scene one with a ff and 300mm and the other with a crop and 300mm and made two prints such that the subjects were the same size on paper in both prints the shutter speeds could be the same, but what we do in real life is make two prints the same size, this means the subjects are bigger in the crop image print so any movement is enlarged more. Nothing to do with focal length, it is all to do with post capture enlargement.
