What you are forgetting is that the effective focal length of the lens is determined by the size of the sensor but it's actual focal length isn't.
Take a 300mm lens on a 35mm sensor camera, the actual and effective focal length is 300mm.
Put the same lens on a DX sized sensor camera, the effective focal length is 450mm while, of course, the actual focal length is still 300mm.
This is because the smaller DX sized sensor only sees a small part of the total image area projected by the lens, effectively making it look like a longer focal length.
However the actual focal length and therefore DOF (for a set aperture) is the same in both cases.
Thus on the smaller sensor camera (the DX one in this case) with a longer focal length lens (effective) you have more DOF than you would on a larger sensor camera with the same effective focal length lens (a real 35mm sensor comparable 450mm lens with have a much narrower DOF than a 300mm lens).
So . . . small compact cameras with tiny wee sensors and very short focal length lenses have very large DOF's (as the shorted focal length the lens has, for a given aperture, the larger the DOF).
Thus, the larger the sensor the smaller the DOF you will have for the same effective focal length, with a giver aperture.
An example - the Canon S90 has a 28-105mm effective lens range, but an actual 6-22.5mm lens range, so you cannot really get shallow DOF . . . even with it's f2 lens . . .
Larger sensors are better in all respects apart from cost.
