I haven't used the "paper towel" method since my very first grows and I wouldn't recommend it now for germinating fresh, healthy seeds.
Due to the delicacy of the emerging seedling and it's rootlet especially, I feel it is much better to start seeds directly in a well-draining soil-less medium like Black Gold seedling mix or Sunshine Advanced #4 (#4 is preferable), Light Warrior, or even rapid rooters. A true soil (like Ocean Forest) can also be used for germinating seeds, and that is what some people reach for successfully but I much prefer starting with a sterile or selectively inoculated mix which is very light on fertilizer like those I previously mentioned.
If you let the rootlet emerge within a paper towel, chances are it will become partially fused with it (after all, it really wants to establish its root system so it can grow vigorously) and you could do some damage by separating and handling it, even if you can't really notice the damage. If this ever happens to you just try to cut the rootlet out of the surrounding tissue with a blade or scissors and be very gentle.
That alone is reason enough for me to dismiss the paper towel method, but there are others. Ultimately I find it much more convenient, for both myself and the seedling, to plant directly into a quality medium. You can help the seedling by planting it in the correct orientation: the rootlet emerges from the more pointed end of the seed (as opposed to the 'butthole' of the seed, where you can see that sort of circular seam) so it is the pointed end you want to push down into the medium. Sprinkle some more soil on top, water thoroughly and have a little patience. The seedling will emerge and the root system can go to work immediately taking in water and nutrients, establishing itself, and forming early symbiotic relationships with beneficial microbes (mycorrhizae, et al) if they are present. Both the Sunshine Advanced Mix #4 and Fox Farm Light Warrior are inoculated with various beneficial bacteria species and mycorrhizae.
Fresh seeds shouldn't have to be soaked in water for any amount of time, or germinated in between paper towels. I see no benefit in either of these methods, except for with seeds that are several years old as the embryo within the seed will begin to dry out after some time. Otherwise the excess moisture could be doing more harm than good and lend itself to early fungal infections such as damping off.