Refer to fig. 1. Let's assume, that the speaker has a cross over frequency of 400Hz. If you feed the speaker with e.g. a 300Hz signal, this will primarily go to the bass unit, but some of it will go to the midrange speaker. So far so good. The problem could be, that the bass speaker, or even worse, the cross over filter for the bass speaker, could be non-linear, leading to harmonic distortion. That would mean, that signals at 600Hz, 900Hz, 1200Hz etc. would be present on the input terminals of the speaker box. These frequencies may only be reproduced by the bass speaker at very low volume, if the bass speaker has a roll off above 400Hz, but the midrange speaker would reproduce them if they were present on the input terminals of the speaker box.
Distortion from the mid/high range is probably less of a problem, because harmonic distortion can only produce higher frequencies, not lower frequencies. Other types of distortion can, but then we are talking about intermodulation, which is a completely different story.
If we then look at fig. 2 with bi-wiring, the situation is different. Distortion from the bass part of the speaker will never reach the mid/high range, since the (ideal) amplifier will short circuit any signals coming back to the amplifier terminals. Thereby, no harmonic distortion from the bass part will be heard in the other part. If however, the amplifier is not ideal, or at least close to ideal, with a very low output impedance, then the situation could be different. This could be the case, e.g. with a tube amplifier with a relatively high output impedance. In this case bi-amping may be needed to separate the signals.