Polarity mystery: Can you help me solve it?

THE BACKGROUND: My speakers are Focal 1007be. They have a Linkwitz-Riley crossover with a 36 dB per octave slope. Because of that, the two drivers are wired with opposite polarity: the woofers are positive, the tweeters are negative.

WHAT I DID: At the advice of a friend with the same speakers, I inverted the polarity of the drivers, by simply reversing the red and black speaker wire leads to the terminals of both speakers, so that the speakers are still in phase with each other, but now the woofers are negative polarity and the tweeters are positive polarity.

WHAT HAPPENED: To my surprise, the sound improved! Specifically, image focus improved. The improvement can't be attributed to the preservation of the absolute phase of the recording, since the improvement was the same for many different recordings (some of which, presumably, preserve absolute phase, while others do not). And the improvement can't be attributed to the speakers being wired incorrectly at the factory, since the friend who suggested that I try this experiment owns the same speakers and experienced the exact same result. So I don't know what to attribute the improvement to.

Can anyone help with this mystery?