The Australian Rugby League Commission (ARLC) now has the power to charge players for on-field acts if they are dissatisfied with the sanctions proposed by the previously independent match review committee (MRC).
Rugby League Players Association boss Clint Newton termed the change "unprecedented over-reach" last week, while four-time premiership-winning Penrith coach Cleary said it implied a "disturbing" lack of faith in the MRC from league bosses.
The rule change comes as the NRL continues to search for consistency between on-field penalties and post-match sanctions for illegal tackles.
Speaking at the launch of the NRL's Beanie For Brain Cancer round, NRL CEO Andrew Abdo insisted the change was only an "insurance policy".
"All it really means is that the Commission is able to, on very rare circumstances if ever, apply to the judiciary to review a matter that may have been missed by the match review committee, or may have, in their view, not been graded appropriately," he said.
"There could be an upwards movement of the grading, it could be a downwards movement of the grading.
"This would be in very rare, exceptional circumstances as an insurance policy. It's not a case of us being in a situation where we're going to see this applied regularly, if at all."
Abdo claimed not to have been aware of frustrated comments made by Cleary, who on Tuesday said it would be better for the NRL to rethink the entire system than weigh in sporadically.
But Abdo said if teams were dissatisfied with the ARLC's charges, they could still challenge proposed sanctions at the judiciary as normal.
"The Commission has no powers to make a final decision, those powers will sit with the judiciary," Abdo said.
Cleary pointed to Scott Sorensen's two-game ban as an example that the judiciary system was making mistakes, with the second-rower escaping on-field sanction altogether for his hip-drop style tackle on Dallin Watene-Zelezniak.
"We'll make no apology for wanting to protect players and we'll also put the onus on the defender to take all measures to avoid those indicators (of a hip-drop)," Abdo said.