No. "In the case of" does not mean the same as "in case of".
In case of fire, do not use the lifts.
In case of emergency, call 999.
I like cats but in the case of Sandra's cat, I'm willing to make an exception.
In addition, "In the case of XXX vs XXX", it's a set legal phrase. It refers to the two parties taking part in a court case of some kind.