Interesting !!! Would not know about the manufacturer's inverting phase on mids/highs, that you would have to ask or check it out with some tech guys.
The results obtained with the bass are normal, and are you absolutely sure that your ears did not trick you, since when there is less bass, the mids and highs will appear to come out more, and vice versa. Maybe you prefer and advantage these frequencies in your personal sound analysis, and it would just mean that your speakers (and/or associated amps) are not very well balanced for your ear preferences.
Another tech reason would be that inverting the bass could be pushing /helping the midrange cone, if the later is not isolated from bass resonance in the cabinet.
The results obtained with the bass are normal, and are you absolutely sure that your ears did not trick you, since when there is less bass, the mids and highs will appear to come out more, and vice versa. Maybe you prefer and advantage these frequencies in your personal sound analysis, and it would just mean that your speakers (and/or associated amps) are not very well balanced for your ear preferences.
Another tech reason would be that inverting the bass could be pushing /helping the midrange cone, if the later is not isolated from bass resonance in the cabinet.