What I don't understand is the statement that's it's a half-truth that a bigger sensor is required for a shallow DOF. Though it may depend on the definition of 'shallow', I think in general it's completely true.
From Prof. Johnson's figures, a P&S has the same DOF at f/3.5 as an APS-C at f/14 or a FF at f/21. But the reality is that many, many P&S cameras have lenses that start around f/2.8 and end at f/8.
Based on Prof. Johnson's example of a 2ft. object at 5ft. from the lens and his formulas, a FF camera at f/2 would have a DOF of about 1". To get the same DOF from a P&S, an aperture of f/0.4 is necessary. Since most P&S lenses start at f/2.8 (many at f/3.5), the best you can do on this example is a DOF of about 7.5" with a P&S.
Sure, if you want a lot of DOF, then a P&S seems to do just as well as a FF. But if you want a shallow DOF, the *only* way to get more of it is with a larger sensor. I suppose someone could make a f/0.4 lens for a P&S, but I'm not sure it's technically possible and certainly not affordable or pocketable. It would have an optical diameter of about 45mm (about the same as my EF 85mm f/1.
and a focal length of just 18mm!