That's nonsense. Just like innocent people with integrity who plead the Fifth. The recruiter will think you're hiding something and you'll be bumped down the list. The analogy of the Fifth is quite appropriate, as the US court system has had bias against defendants who might/do invoke that right. It was only in the previous decade that the Supreme Court made a definitive ruling (in a liberal interpretation of the Fifth) about the subject.

The only integrity involved is the integrity I have toward myself and my goals. The goals of the company are ancillary.