Roughly speaking, if the control loop is dominant-pole compensated (it is, more or less), then the controller has a phase shift of 90 degrees in the cutoff band.
A pure integrator "plant" (the capacitor's impedance) has a phase shift of
90 degrees as well, hence oscillation (or at least something near it, give or take accidental zeroes or additional poles, pushing it one way or the other).The only way to stabilize such a system is to push one pole up or down so far that the other no longer has 90 degrees phase shift.
This is usually done by reducing C or adding R, restoring phase margin. He's just demonstrating that it can be done the other way -- brute force.
In practice, a real 300mF (not uF, also, 10^-1 s) capacitor may have enough ESR and ESL (including wiring) that its impedance is not actually that low, even at low frequencies. Doesn't matter; the controller is theoretical (a simple SPICE model), as is the capacitor, so it serves nicely to illustrate theory rather than practice.
The 1 / (2*pi*(10Hz)*(0.3F)) ~= 0.05 ohms corresponds to...drumroll please... the DC output resistance of the regulator, more or less. :-)
Tim