Crossing Left and Right Speakers

Agree with you OP, it will just reverse L and R sides of soundstage

I think this was probably meant differently.

They probably meant to refer to toe-in, or, how much the speakers are angled relative to the rear wall. With the speakers flat to the wall behind them the tweeter axes (plural of axis, say axe - ease) are parallel, but as we angle the speakers in (more toe-in) the tweeter axes cross, either behind or in front of the listener.

Extreme toe-in where the axes cross in front of the listener, can help when speakers are placed very close to side walls.

Changing toe-in can affect the imaging and leave you in one of these situations:

• You hear a L and R but no center
• You hear a L and R and center but the space between seems hollow
• You have a clear image from speaker to speaker with no gaps

By the way, most listeners use too much toe-in. Many speakers sound better with no to modest toe-in instead of being pointed directly at your ears.

I just experienced this the other day.  I have a recording for Audiogon made by the Chesky label (available from HD tracks) that has some really good imaging effects.  On the St Louis Blues cut, there are numerous instruments that appear either to the left or the right of the loudspeakers.  I had changed some gear around in my system and unintentionally switched the channels.  I knew immediately something was off - the instruments were still outside the loudspeakers (but on the wrong side), but to your point what I noticed that surprised me was that there was nothing in the center of the stage, only on the outsides.  There’s another track where a flute travels laterally around the soundstage, from left to right and back again.  In this case I couldn’t track it.  My speakers were wired in phase.  I suspect on a lot of recordings, other than switching left and right within the soundstage, there will not be a huge impact otherwise.  But I guess some recordings are different?  Not sure why or how.

Left speaker to Right shoulder. Right speaker to Left shoulder.  That's all.  

My local AudioNote dealer does this with a few systems setup there.  In some ways it works, and other ways imo it can be confusing how it sounds.  Try it and see.   

Generally, direct sounds from LR speakers don’t reach to a listener due to angled woofer cones. More toe-in can result less direct sounds. To hear more direct sounds, move ears(head) closer (5~7ft) to speakers. Alex/Wavetouch