If they did rot then they wouldn't be there to use as an indicator at all would they :-)

I think the thing with them (if it's anything at all) is that there was a lot of them.

We all aagree that the flying ants do their thang in August, yes? If the turf was cut the following May, for instance, then a lot of the dead flying ants would have been eaten, so there wouldn't be many around, would there?

If the above assumption is correct then if there's loads of flying ants in the turf then it is a fairly safe bet that it wasn't cut too long after August, isn't it?