Right. The configurability is entirely in the "data path", but control of that configurability is not. The control of the satellite is a separate band, bandwidth, rate, etc, called TT&C (Telemetry, Tracking, and Commanding)
So basically there's a "bootloader" which can be used to upload new "ROMs" into the payload? Sounds like a sensible way to do it.
It is even simpler than that: you've got a computer for the platform, and another one for the payload. You send commands to the platform computer over the TT&C frequency at a few kbps.
You can also update the platform OBC as well, with its bootloader then selecting which SW image to use.