<steps in authoritatively>
No, the REAL rule is: Only one ship or unit (or unit group in early Versions) can mine a planet or asteroid sector at a time. (That's right, planets can be remote mined, but only if they are uninhabited. No, they do not need to be colonizable or breathable.) So the best strategy is probably to build a starbase with about 20 remote miner components (or however many will fit) over each asteroid sector you want to mine. (Bases have a 50% maintenance reduction, which is QUITE useful for a remote miner.) Or, you can use large satellites, which have no maintenance at all, but unless you are playing with a really outdated Version, only one satellite will be able to mine in each sector. So you want a satellite layer with only 1 sat launcher so you don't go wasting satellites all over the place. If you ARE using the old Version (maybe 1.30 and before, I don't remember), just plop about 100 sats over the asteroid sector and watch the income roll in!
Oh yes, and if you get lucky and find a planet with moons that are also rich in resources... your miners will mine their full capacity from EACH planet or moon... don't ask how they do it, but they do!
<steps off pedestal>