Yes, that's quite true. There is mathematical proof that even passive bi-amping can have an effect on the reproduced signal. It has to do with the way the speaker wire reacts with the load of the crossover. Of course the links must be off at the speakers. It can probably even be measured. But you are also quite correct in that the effect is so miniscule it would never he heard nor does it warrant any discussion in a real world system.
On a practical level a proper bi-amped system uses a line level crossover. Anything else is just audiophile folklore.
P.S. I run biamped LCR using a Behringer 2496 - great unit. My mid amps are DIY 70W tube KT88 PP and my tweeters are 10w 6V6PP maps. My subs are off a rebuilt Phase Linear 700.
And no, tubes are not better than transistors. I just like the old stuff