I doubt that you could use a Tesla-like Supercharger to charge a battery other than one made by Tesla. I'm not talking about DRM, I'm talking about the architecture of the battery pack itself - its charging characteristics, its safety features, its cooling system, and so on down to the level of the individual 18650 cells.
Disclaimer: I know nothing about the Tesla Supercharger.
But I do know generally how chargers work - specifically multi-cell lithium chargers. Each cell requires a charge management circuit. I don't think the Supercharger actively manages the cell level charging. It is highly unlikely that given 10s or 100s of cells in a Tesla pack that there is going to be anything other than voltage, current and maybe a serial data line for that can be used for metering and financial charging.
As long as my car can handle the voltage, draws an appropriate amount of current and (possibly) provides some identification for payment or statistics, I can take that power and charge 18650's, NiCds, SLAs, caps or just run a big stereo for a block party. At some point there may be a $/kWh bill in the mail, but otherwise, the charging station is most likely battery tech agnostic.