This has virtually nothing to do with the type of fabric used or your anatomy. It's a result of the pattern used to make the underwear. The briefs shown in these examples all have a center seam, which is used to create the pouch. Take a close look at the fabric along this seam. At the bottom where your balls sit, the two pieces of fabric joined along this seam are pointed away from each other. As the seam moves up, the pieces of fabric are rotated to align, and maybe even bend in to face each other the opposite way. This creates a three dimensional shape, unlike traditional briefs which are sewn flat along the front. And this is what is creating the phantom bulge. You will be hard pressed to find the phenomenon on traditional briefs.
All clothing gets stretched and worn to some degree, but your briefs are just showing off their clever design when you're not in them not a permanent imprint of massive manhood.