What I have found, and makes sense, is that the skinny string is lighter....travels faster, so it does require a stiffer arrow in most cases. My spine requirement jumped one size. Your mileage may vary.
Obviously the point of diminishing returns is always a concern; how skinny is too skinny, how fat is too fat. Luckily we have folks out there who have already been testing string material for awhile, and I defer to them initially, then see how they work for me.
Skinny is relative also. If you are shooting a big 70 pound bow with 16 strands of dacron, a 12 strand would seem skinny to you.
As long as you don't cross that line of safety, you should be fine. You see it's not just, fat or skinny....or light or heavy, there is a medium out there that will work well. If you like fat strings, by all means use them; same for skinny ones...it's not wrong, just different.