I never tested the Parasound with both hooked up when I owned the amp. This new great idea :) is brand new.
Here is a comment from an amp manufacturer that I just asked.
- bridgeable amplifiers are sometimes an exception. I think you'll find that quite often that switch isn't switching the input so much as it is making sure that the unused phase of the XLR connection is grounded so it won't make noise.
Some solid state amps use an entirely different circuit to convert from balanced (usually using an opamp) to single-ended and then apply that to the regular single-ended input of the amp. Such amps might also have a switch. IMO this is a poor way to execute a balanced input; if the actual amplifier itself is balanced that seems to work better.