Directly from the Audioholics article.
10) Myth: high-level speaker connections to a subwoofer is superior. You get better integration and time alignment.
Pursuing the Truth: Just a big No! This is nonsense.
A high-level (Speaker level) connection is no different than a low level (RCA or XLR) connection. The time delay in an amplifier is minuscule and adding it then adds more time delay to the amplifier in the subwoofer. Why would that be good? Amplifiers often have higher noise and distortion than preamp outputs so this could make things sound worse.
However, for the most part, there is no difference. The intuition that many use to justify this improving Integration lacks logic. Integration is and always will be about the crossover, level, phase, delay, and placement. Incidentally, connecting a subwoofer high-level or speaker level, negates the bass management in the AV receiver or processor and thus you'd have to activate the internal LPF of the subwoofer. Bass management is usually best done in the digital domain on the AV processor/receiver side, not at the subwoofer itself.