Hi river,

A splendid question, and I am afraid the answer is not equally spectacular. It turns out that the Bode plot
(or phase and gain margin, so to speak) provides a correct estimate of system stability under some
very special assumptions.

It so happens that circuit designers often deal with such systems, and hence we are conditioned to treating the
Bode plot as sacrosanct.

One should always use the Nyquist criteria(if simulating) or a root locus, especially when dealing with complex systems.
I have mentioned this in an earlier post somewhere on this forum.

For the example you present, the Bode plot fails spectacularly. However, the system is conditionally stable outside
a range of gain values. This particular example and other discussions on the merits/risks of using different stability
measures are discussed very well in most control systems books, and also in Thomas H Lee's book on "CMOS RF IC Design"
where the example quoted by you should also be found.

Regards
Vivek