That quote is not correct. They are talking about two different things.
Grit is small rocks or large pieces of sand they eat to crush their food in their gizzard. They don’t have teeth to grind up their food like we do so they use rocks in their gizzard as teeth. They can use whatever rocks they can find as grit. The harder rocks last longer, maybe as long as a month if they start out larger sized, but they all eventually get ground down and pass on through their digestive system.
Oyster shell and egg shell are not suitable for grit. Egg shell is too soft, it just goes on through the gizzard after being crushed. Oyster shell is practically all calcium. The chicken’s digestive juices are acidic and will dissolve the oyster shell, so it doesn’t work either for very long. Oyster shell or egg shells are meant to give laying hens extra calcium they need for their egg shells. Unless they are laying eggs chickens don’t need a lot of extra calcium. Too much calcium could be bad for them, but all chickens that eat anything other than the prepared commercial chicken feed need grit to grind up anything hard they eat.
If you are feeding Layer, which should have about 4% calcium, they probably don’t need extra calcium to start with. They can also get a lot of calcium when foraging if you have limestone rocks they will use as grit, but also form some plants and creepy crawlies. You can let your egg shells tell you if you need extra calcium. If the egg shells are soft or thin, you should offer extra calcium on the side. That can be oyster shells or egg shells. Hens that need it generally know to eat it and those that don’t need it know not to eat a lot of it. If they are getting enough calcium from other sources, they may not eat the oyster shell or egg shells because they don’t need it. It does not hurt anything to offer extra calcium on the side. If they don’t need it, it may last a real long time.
You will get a lot of different opinions on how to treat egg shells if you feed them to the chickens. Some people do all sorts of things dry them, clean them, cook them, and crush them, worrying about the chickens becoming egg eaters. Some of us just toss the opened egg shells where they can get to them without cleaning, drying, or crushing. If you are more comfortable crushing, cleaning, cooking, and drying the shells, by all means do that. It won’t hurt a thing.