No it's more like
1DX+$6000+firmware = 1DC
But yes, the 1DC does everything the 1DX does in terms of stills it just shoots 4K video in addition to that. Canon says they did stuff for heat dissipation but that could mean one extra screw or completely redesigned parts, I'm not sure.
Yes the price increase is bogus, but there's definitely physical improvements to allow the camera to output that kind of high bitrate high res video, even with 1080P on the other DSLRs they struggle with overheating, but even with quality components added for heat dissipation I don't see any of that adding beyond $1K.
Also, EOSHD reports disappointment with a test shoot using the 1DC, rather soft output similar to how the 5DMarkIII video looks, doesn't make any sense...