The last circuit, in steady state, behaves exactly as R2, but when the signal changes, the current through the capacitor is the derivative of the signal, reducing the amount by which the circuit is just R2.

I speculate it acts like an inductor because that would be a logically silly thing for it to do but I'm not doing the math at 1am on my phone.

I've always admired lcamtuf.

Wait until he hears about negative Miller capacitance.