The throw rug over hardwood is advised for several reasons.
1) Stability: if part of the floor is uneven, this can prevent unwanted buzzing
2) Acoustics: Dr. Hsu says that it improves acoustics--for the same reasons you would use Sonex or sound absorbing foam.
3) Protection: the rug protects the floor, which is also very useful if you want to slide the subwoofer to another position
4) Decoration: you can match the throw rug color to nearby objects.
Will the rug muffle the sound? Well, bass acoustics are very unusual and counterintuitive. Bass is only stopped by dense things like sand, solid wood, or gas filled membranes. Throw rugs have nowhere near the depth to absorb any sound the subwoofer produces.
Basically, the bass goes through the rug, hits the floor, and spreads in every direction inside the room. It is omnidirectional--it goes in every direction even though there is a rug underneath.