Sort of, yes. In order to keep the design small and affordable, the game ROM and save RAM are actually in the microcontroller rather than separate components on the board. But essentially yes, DK Remix does not use the DK ROMs.
The microcontrollers come in various ROM sizes, and the largest of them would actually be able to hold 7 versions of DK (depending on ROM size - Remix is larger than DK, and some of the space on the chip has to be used for firmware.)
Yes, the board works just fine on DKjr hardware, so if it were loaded up with DKjr ROMs, it could be used to run alternate versions of DKjr too.
But, it can only change program code, not graphics data or sound code. So, we couldn't actually run Herbie at the Olympics or that Pool game as Chris P joked about. Stick a DK Remix board into a DKjr. PCB and it'll boot up Remix... but it's going to play with Jr. graphics characters... all mixed up graphically.