There are lots of different opinions about this, as you say, but seed eating birds often eat grit which helps grind up the seeds in the bird’s gizzard as well as contributing minerals to the bird’s diet. The best thing probably to do is to put some grit in a small bowl in the bird’s cage, allowing your bird to eat the grit if your bird wants to.

Oyster shell grit is soluble, and breaks down in the acid environment of the bird’s gizzard thus letting the mineral be absorbed. Mineralized grit is insoluble, and so stays a longer time in the bird’s gizzard. Some birds can eat an abnormal amount of grit, or eat it at odd times and in these cases it is best to get your bird checked out by a vet.