I honestly don't think it has anything to do with the fabric. The rolled edges may play a part, but I don't have a non-rolled example to look at.
Below is a picture of a standard woven silk jacquard, sorry for the crappy picture, you can see the roll pretty clearly though.
If you see this video of how Drake's ties are made, watch around the 35 seconds mark and about 1:24, you'll see how they press the ties. Tie Your Tie do not do this at all.