Shimon,
As I said, there are several definitions of the term tzaddik, depending on the context.
The definition that you gave is the one that is brought in Tanya and proven from many mamorei razal.
However, the Alter Rebbe (Baal Hatanya) himself acknowledges that the term is sometimes used with other meanings (like in the Rambam quoted by smerel, or ??????? ?? ?????, etc.).
Re Morahs (I reply with a grain of sensitivity just in case you are suffering trauma from your kindergarten morah):
Don’t be so quick to condemn. Remember the ????? ????”? (brought in ??”? ???? ??? ???? ??):
??? ????? ???? ??? ??? ????? ?????? ???? ???? ???? ????? ????? ?????? ?????? ????