Be careful with store bought grit, especially grit in the pet shops. It can contain a lot of calcium and excess calcium can harm the baby chick's liver. Not that the chick will immediately fall over dead the instant it eats an oyster shell, but over time too much calcium can cause serious problems. Save the extra calcium until they are laying and can use it.
I like to wait until the chicks are 3 or 4 days old to give them grit, simply so they know what their food is. Some of them will still eat a lot of grit but it just passes through their system. As long as they are eating their food too, they will be OK. That farmer's tale about not giving them grit makes sense to me if all they eat is grit, never eating their food. Then they would be starving to death, eating a lot of grit trying to get some nutrition, and impact their crop or gizzard. I've never had that problem, but I guess in theory it could possibly happen.
I sometimes take fine sand from my gravel road or driveway to give to chicks in the brooder as grit. Sometimes I take dirt from the run where the older chickens are. If your driveway or gravel road is salted for ice and snow, I would not use it since their systems cannot handle the extra salt. I give them dirt from the run so they will get the cocci protazoa that their parents have while they are still young enough to develop an immunity to it.
Coarse sand like construction sand is better than play sand. The angular coarse sand is in bigger pieces and its shape helps it gring their food up better in the gizzard. The play sand will work, but they have to go through a lot more of it. Adult chickens can use pieces of gravel up to the size of a pea, but they also use smaller sized pieces along with it. If you cut open the gizzard when you process a chicken, you will find a few larger pieces of grit and quite a bit of sand sized pieces. If all they have is fine sand or dirt, they will use that, but they have to go through a lot more of it. Baby chicks cannot handle grit the size of peas. They need smaller pieces, like in construction sand. But they grow fast and can soon use larger and larger pieces.