late 14c., "explanation, spoken or written remark," from Old French coment "commentary" or directly from Late Latin commentum "comment, interpretation," in classical Latin "invention, fabrication, fiction," neuter past participle of comminisci "to contrive, devise," from com-, here probably an intensive prefix (see com-), + base of meminisse "to remember," related to mens (genitive mentis) "mind" (from PIE root *men- (1) "to think").
The Latin word meaning "something invented" was taken by Isidore and other Christian theologians for "interpretation, annotation." No comment as a stock refusal to answer a journalist's question is first recorded 1950, from Truman's White House press secretary Charles Ross.