The 2002 U.S. Amateur champion finished the day just nine points off the lead, held again by England's Steve Webster. Barnes had been informed he was under investigation for allegedly improving his line during the second round.
An e-mail, sent overnight from a golf fan in the United States, had claimed Barnes swept sand from the fringes of the green on the 11th hole, where he landed after splashing out of a nearby bunker on Friday.
The 23-year-old insisted he had simply been removing burnt Bermuda grass from his path.
Barnes went out Saturday in a round of 64 which, translated into the modified Stableford format, earned him 16 points.
Webster, the halfway leader, shot a 67. With 39 points total, Webster leads Australian Nick O'Hern by five.