Asymmetrically?

In all likelihood, not placed symmetrically around the listening axis. In other words, if you have a 20 x 30 room, don't place them on the front wall each 2' off the wall. That would be a symmetric placement... Can't speak for their theories, however. Give it a listen and see if it makes a difference.

"give a listen and see if it makes a difference"----yes, and I agree.

If the main speakers (with their own subwoofers) are placed symmetrically why should the external subs be positioned asymmetrically?

I own two subs, each is positioned directly behind the corresponding front main speaker and (if properly dialed-in) there are no "audible" standing waves. (Forgive me if the latter is not acurate but, I am assuming a standing wave would create boomines in the room. Please correct me if I am misinformed.)

Not for a symmetrical room. In fact if you read Todd Welte and Floyd Toole's paper on subwoofers, you will find that placing two directly opposed to each other has a very interesting effect on standing waves. Where the peaks would normally occur the two are working against each other and where nulls would occur, they actually are working together and bringing the nulls up. It gives a large area a flatter response. They went on to show that 4 subwoofers can optimize this. The simulation went from 1 to something like 5000 subwoofers.

Here's a link to the article:
[url=http://www.harman.com/wp/pdf/multsubs.pdf]Multiple Subs[/url]

Very interesting report on sub placement, everyone should read it. Thanks for the link.
Rock on!
G