That's horrible advice. 22lr and 22 mag have different diameter bullets, as well as cases. Fire a 22 LR in a 22 mag chambered firearm, and you're asking for trouble. The case could swell and stick, rupture, etc. Stick to firing ammo in the gun that was made for it, and you won't have any issues.
I've probably shot hundreds of 22lr rounds out of a 22 mag. I wouldnt recommend it and certainly wouldnt do it again knowing what I do now. But the gun still shoots great and never has had an issue. Now I have a 22lr and a 17hmr that look very very similar to the untrained eye. Well mom decided to shoot a woodchuck in the yard one day with the "22" well turns out a 22lr bullet will get lodged 3/4 of the way down a 17hmr barrel.
I don't believe the .22mag has a different diameter bullet than a .22lr. I have two revolvers that have a .22lr and .22mag cylinders with them that you can swap. Both are plenty accurate, meaning the bullet isn't flopping down the barrel as different diameter bullets would do.
That being said, I don't think it is safe to fire .22lr or .17hm2 out of the bigger brothers.
They do. Your pistol has a slightly larger bore, to accommodate the mag. Regular 22 shells will still shoot accurately sometimes, and sometimes not at all. Your best best if you want an accurate 22 lr is to buy a pistol chambered for just that. Say you have a single six that came from the factory with the interchangeable cylinders, and a single six in 22lr only. You can't get a 22 mag cylinder fitted for the single six chambered in 22 lr, because the bore is too small. Your gun came with the larger bore to alleviate that problem. Normal bore diameter for the 22lr is .222-.223. 22 mag is .224