The problem is the Steam Distribution Agreement isn't public so I don't have a way to prove if this is true or false.

At the same time there are articles like this https://www.bbc.co.uk/news/articles/cx2g1md0l23o on the bbc claiming a tribunal ruled a case can continue against Valve for "forcing game publishers to sign up to conditions which prevents them from selling their titles earlier or for less on rival platforms".

The website for the law firm clearly states the price parity is not just for steam keys https://steamyouoweus.co.uk/the-claim.

If there was no evidence it would be thrown out. But until it concludes who knows what the truth is.