The bias thing is absolutely relevant, plenty of well documented scientific evidence. Speaker sensitivity, impedance, distortions, all vary with frequency; and room acoustic environment has significant impacts as well. However, the amp's job is to amplify, when operating well within their optimal operating limits, amps that are designed for truly high fidelity applications will have almost ruler flat frequency response, with damping factors high enough, distortions low enough, to get out of the way of other components and factors that have much more impacts.
I have used REW and the UMik-1 mic to plot my speakers response when paired with different preamp/amps, the plots practically overlap to the point they look like one. Anyone who owns an AVR and amps, or prepro, preamp and power amps can easy do the same to see for themselves.
There is one exception, when one of my vintage preamp is involved, I do get some slight variations, enough for me to investigate further, when I have some free time.