It's not just the pixel size, although it is contributory. The issue exists even for film cameras.
Aperture is the size of the hole through which the light must pass. It is expressed numerically as the relationship between focal length and the diameter of the opening.
e.g. A 10mm opening with a lens with an 80mm focal length yields a designated f-stop of 8. If I double the area of the opening it will result in a diameter of 14.15mm. The resulting f-stop designation will be 5.6.
Since the f-stop designations are relative, the smaller lenses of digicams require smaller actual openings for the same f-stop designation.
e.g. The CP5000 at a focal length of 7.1mm requires an opening of .89mm for an f-stop of 8.
Now, the reason we don't see higher f-stops on digicams is two fold: 1) The smaller the phyiscal size of the aperture blades, the more difficult it is to precisely control their positioning, especially on an adjustable aperture cameras. 2) The primary difficulty as outlined by herbko is diffraction. The smaller the actual opening, the more diffraction. It is dealing with this diffraction that limits the use of usable smaller f-stops.
The pixel size and density of pixels contribute to the camera's ability to deal with the diffraction problem, as does the glass itself.
Of course, because CCDs are smaller than 35mm film, the need to stop down for greater DOF is greatly reduced.