It takes about 25 hours for an egg to make it through the hen's internal laying factory from the time the yolk starts its journey until the egg is laid. There is nothing that says the next egg cannot start before the first egg is laid. Some hens lay about the same time each day, which means that the next egg starts just before the first egg is laid. Some seem to lay a bit later each day, which shows the second egg starts about when the first egg is laid. I don't know if there is a trigger there or not. I think it is simply that hens that start eggs about 24 to 25 hours apart live and reproduce to pass on those genetics.
Sometimes a hen's internal egg factory does not function properly. She starts two yolks fairly close together, or at least not a day apart. If they are close enough together, you may get a double yolked egg. If here is a little more space between starting times, she may lay two eggs in one day. In this case, the second egg usually has a very thin or soft shell. The shell gland does not have enough time to secrete enough shell material. This has nothing to do with how much calcium they are eating. The shell gland simply does not have enough time to secrete enough shell material for this second egg.
It is quite possible for a hen to lay two eggs in a day. It is possible that the second egg could even have enough shell on it that you don't notice it is a little thin, say if the second egg is laid several hours after the first. I can accept that on a rare occasion, a hen may lay two decent eggs in one day, but I do not accept that it is normal for a hen to regularly lay two well formed and developed eggs regularly. I certainly do not accept that a hen will lay more than two well formed and developed eggs in a day.
I don't necessarily believe that someone is purposely passing on bad information when they report that. I just consider them confused about where the eggs came from.