I'm just guessing here but if your neighbor grew up on a farm, it is possible it was one of those that actually supported the family, not just a "hobby farm" and since they had jobs to do all day, they probably did just gather the eggs in the AM because that was when they needed them and they didn't check the rest of the day. Hence, all the eggs, in there from throughout the day, at 6 AM sharp. They probably never even thought about the fact that all the chickens didn't lay at the same time. He is just "remembering when" and assuming what seemed to be the case, like the world being flat and all. Honest mistake I reckon. 
Just goes to show that the chickens can handle not being checked that often, even if we can't, LOL!
I swear, the one silkie hen I have that actually lays right now (my other 16 pullets are only 10 weeks), won't lay if I am trying to see it happen. One night, I swore she was about to lay and I sat there till it was dark and she was snoring on her roost so I gave up and when I went out to look the next morning about 6:15 or 6:30 and there was the most beautiful little tan egg, taunting me.....