Gertrude says "The lady doth protest too much mee thinks." This comment comes during the play-within-the-play, where the actor playing the part of Gertrude professes (protests) her love for her first husband. Gertrude, realizing that she was nowhere near that faithful to Hamlet's father, says that the actress is over the top.
So the line does not mean that one who strenuously professes their innocence is betraying guilt - if anything, it means the opposite.