Actually it's very arguable. The depth of field of say a 100mm lens working at f/8 and focused to say 3 metres is dependent on one thing and one thing only: the circle of confusion allowed in the design. The field of view (frame size) does not come into the equation at all. The issue here is that a smaller format will usually mean that you're magnifying the image more when you view it, so smaller formats need a tighter circle of confusion and consequently appear to have less depth of field. Now, if you're talking about the smaller format camera having the same field of view, the focal length is shorter too e.g. you need about 60mm "real" focal length on an APS-C camera to get the same field as a full frame camera using a 100mm focal length lens. And now, with the same aperture and working distance selected, the smaller format camera will appear to have much more depth of field - just as a crop from the full frame camera mounted with the same 60mm lens working at the same aperture and the same working distance would have more DoF than the same area imaged with a 100mm lens.