Cornet slipped off her shirt, revealing a black sports bra, after realising she had put it on back to front while off court during a 10-minute heat break before the third set of her first round defeat against Sweden's Johanna Larsson on Tuesday.
However, there was a storm of criticism for umpire Christian Rask's decision to issue a code violation to 28-year-old Cornet while male players were free to change shirts to combat Tuesday's 38-degree heat.
"All players can change their shirts when sitting in the player chair. This is not considered a Ccde violation," said organisers in a statement issued Wednesday.
"We regret that a code violation was assessed to Ms. Cornet yesterday. We have clarified the policy to ensure this will not happen moving forward. Fortunately, she was only assessed a warning with no further penalty or fine.
"Female players, if they choose, may also change their shirts in a more private location close to the court, when available. They will not be assessed a bathroom break in this circumstance."
The tournament was blasted for double standards over the Cornet incident, especially as it came just days after the French Open said it would ban Serena Williams from wearing her 'Black Panther' bodysuit again at Roland Garros.
"Alize Cornet came back to court after 10 minute heat break. Had her fresh shirt on back to front. Changed at back of court. Got a code violation. Unsportsmanlike conduct..... But the men can change shirts on court," tweeted Judy Murray, the mother of former world number one Andy Murray and a leading coach and respected voice in the sport.
Former Australian player Casey Dellacqua replied to Murray's tweet, saying the decision was "ridiculous".
The WTA sais the code violation handed to Cornet was "was unfair and not based on a WTA rule, as the WTA has no rule against a change of attire on court".
A spokeswoman added: "The WTA has always been and always will be a pioneer for women and women's sports. This code violation came under the Grand Slam rules and we are pleased to see the USTA has now changed this policy. Alize did nothing wrong."
Many on social media were quick to point out that just a few hours after the Cornet incident, Wimbledon champion and two-time US Open winner Novak Djokovic sat courtside on Arthur Ashe Stadium with his shirt removed and with an ice towel draped around his shoulders.
Last week, French tennis federation (FFT) president Bernard Giudicelli sparked claims of sexism when he banned Williams's black body suit from next year's Roland Garros.
"You have to respect the game and the place," said Giudicelli who added there will be "certain limits" on clothing for the 2019 French Open.