I've been in the right seat when the captain had the exact same issue. His contact just popped out during cruise, and he spent 10 minutes trying to put it back in so it would stay. He acted like he would be completely ineffective flying the airplane with one eye, and I wound up doing the landing even though it wasn't my leg, since by the time he got it in it was so dried out he couldn't see. I was junior to him, so I couldn't come right out and ask him WTF he didn't carry a pair of glasses with him as a backup.
By then it had already changed, but when the FAA first began accepting contacts as approved corrective eyewear (mid-late 70's, I think) you were explicitly required to carry a pair of glasses on your person in case this very thing happened. It seems that requirement disappeared sometime in the last ten years.
And before it gets brought up, as a general rule if your glasses and contacts are the same prescription, you should be able to see just fine with contacts on underneath, so it's not like he would have to dig the other one out. The F-15 pilot should have just stuck his glasses on and rolled on, no big deal. Instead he had to make a big fuss (maybe he wasn't carrying his glasses like he should have been) and will probably be asked some hard to answer questions by his squadron cmdr when he debriefs.