I think I fired thousands of rounds of .22 LR thru a .22 Mag rolling block when I was a kid. Never knew we weren't supposed to. The larger case size on the .22 Mag is to keep people like me from trying to stuff them into a light .22 LR.
Not quite. A lot of folks think the .22 Mag is based on the .22 LR like the .357 Mag is based on the .38 Special. Not so much. The .22 Mag or as it's properly known, the .22 Winchester Magnum Rimfire is base on the older and lesser known .22 Winchester Rim Fire, or .22 WRF. The .22 WRF was designed for the Winchester 1890 Pump Action Rifle. It's considered obsolete by today's standards, as there are hot loaded .22 LR's that are pushing a similar weight bullet at higher velocities.
In short, the .22 Mag is no more based on the .22 LR than the .17 HMR.