Counterintelligence polygraphs are routinely scheduled for Top Secret/SCI security clearance holders in positions with access to classified intelligence information. In a recent Defense Office of Hearing and Appeals (DOHA) case, the applicant was initially denied continued eligibility for his clearance because of trying to beat the polygraph results, using breathing techniques to throw off control question baseline readings. Go here to read the highlights of the DOHA appeal.
Do they ever use polygraphs for Public Trust determinations?
No. Polygraphs are only used in connection with positions requiring a security clearance.