Cl- is a reducing (not oxidising) agent for KMnO4. (Or my chemistry english is getting bad)
I'd say it's because of the same reason. K2Cr2O7 is a strong oxidiser.
Oh, and when they reduce, H+ causes them to reduce to lower oxididation states. In H+, permangate MnO4- reduces to Mn2+, while in OH- only to MnO42-