This was allowed as late as the 2019 season per NCAA Casebook.

REVERSE REFEREE POSITION..... Is there an offensive starting position called the reverse referee position? Example: If the top wrestler is starting on the right-hand side of the defensive wrestler, the top man would be facing backwards, placing their right arm around the waist, their left palm on the defensive wrestler’s right elbow and one or both of their knees down on the opponent’s right side. Is this starting position legal? RULING: Yes, this starting position can be considered legal as long as the following rules requirements are adhered to:(1) The palm on the near side is on the elbow; (2) The hand around the waist is placed loosely around the waist and on the navel of the opponent;(3) One or both knees, on the near side, are down on the mat; and(4) The head of the offensive wrestler is on the defensive wrestler's back at the midline or above. If a wrestler attempts to utilize this starting position and all four of those requirements are met, the starting position is correct. As in the case with all starting position violations, if one or more of the requirements is not met then a caution is imposed.