I don’t know how it is at your grocery, but I go shopping very early when the store opens and have often seen the Krispy Kreme delivery person bringing in new stock and removing the old. Granted, I don’t know if this is a daily occurrence because I shop weekly, but it doesn’t seem to matter what day of the week I go, they are there. They don’t stock a huge amount either, maybe a dozen boxes go on the display (a combination of six and twelve donut size boxes). They don’t seem to have to remove many boxes either, just one or two at most. So I think the product in our stores is pretty fresh.
I don‘t buy the Krispy Kreme donuts though. I prefer the store bakery brand when grocery shopping, or Dunkin if I am making a special trip.