A common (and arguably idiomatic) allusive expression is methinks he [or she or they] doth protest too much. The source of this expression is Shakespeare's The Tragedy of Hamlet, Prince of Denmark, where it appears in a somewhat different form, during a critical scene in which Hamlet has arranged for the (new) king and the queen to watch a play that reenacts what Hamlet suspects actually happened in the events leading up to the murder of his father, the previous and rightful king of Denmark:
Hamlet[ to Queen Gertrude]. Madam, how like you this play?
Queen. The Lady doth protest too much methinks.
At this point in the play within the play, the "Lady"—who is acting out the same role that Gertrude played in real life—has been effusively professing her extreme devotion to her husband, who is soon to be murdered by his brother (who then usurps the the throne), with the queen's connivance.
The sense of the expression is that people characterized as "protesting too much" are overdoing their show of innocence or virtue and thereby inadvertently hinting at their dishonesty or lack of virtue with regard to the matter under discussion.