There is a reason why leaving seeds sealed in a bag between wet paper towels for a week isn't a great idea... people forget that plants respire aerobically (germinating seeds and seedlings too). Their cells breathe; root cells breathe and require oxygen. A seed that is slow to germinate is more likely to rot between paper towels.
Quality healthy seeds will sprout in relatively little time with warmth, moisture, darkness. So yeah, healthy seeds will germinate between wet or moistened paper towels, usually in good time. This really isn't practical (ideal), though and becomes less so the more seeds you're planting. The only 'benefit' to using paper towels is you might get to find out a little sooner that your seed germinated, at the cost of fussing with it more afterwards.
Good planting media\soil\soil-less mix in 16 oz solo cups, pre-moistened and then watered thoroughly after seeding offers all of the benefits of the paper towel method, plus good planting media remains aerated when wet (allows for gas exchange), keeps the seed in constant darkness until sprouting (even with lights on above), provides immediate access to nutrients and symbiotic organisms. If it dries out too quickly, you are likely not watering thoroughly (moisten then water if dry), don't add any additional perlite, or use a larger container if you live where it is particularly dry.
BTW if your seeds rotted... roll them between your thumb and forefinger; if they fruitlessly get squashed they rotted. A healthy\mature seed shouldn't break during this test, even if you're applying some pressure.