The Premier League "needs to re-examine the assurances" it was given about potential Saudi state control of Newcastle United, says human rights group Amnesty International.
However, in a US court case Newcastle chairman Yasir Al-Rumayyan has been described as "a sitting minister of the government" with "sovereign immunity".
The statements have been made by lawyers representing LIV Golf, owned by the PIF, which also has a controlling stake in Newcastle.
"It was always stretching credulity to breaking point to imagine that the Saudi state wasn't directing the buyout of Newcastle with the ultimate aim of using the club as a component in its wider sportswashing efforts," said Peter Frankental, Amnesty International's UK economic affairs director.
"There's an unmistakable irony in the sovereign wealth fund declaration emerging in a dispute about another arm of Saudi Arabia's growing sports empire, but the simple fact is that Saudi sportswashing is affecting numerous sports and governing bodies need to respond to it far more effectively.
"The Premier League will surely need to re-examine the assurances made about the non-involvement of the Saudi authorities in the Newcastle deal, not least as there's still a Qatari bid for Manchester United currently on the table."
The Premier League has declined to comment.
A San Francisco court has approved the PGA Tour's request to include Al-Rumayyan and the PIF as defendants in its lawsuit against LIV and ordered them to produce documents in the case.
However, the PIF is challenging the order, arguing the fund and its governor Al-Rumayyan "are not ordinary third parties subject to basic discovery relevance standards".
"The order is an extraordinary infringement on the sovereignty of a foreign state that is far from justified here," a court document reads.
"They are a sovereign instrumentality of the Kingdom of Saudi Arabia and a sitting minister of the Saudi government, and they cannot be compelled to provide testimony and documents in a US proceeding unless their conduct - not LIV's or anyone else's - is truly the 'gravamen' of the case."
The PIF initially withdrew from its takeover bid for Newcastle in July 2020 as a result of an "unforeseeably prolonged process", before the deal was revived.
The takeover was only approved in October 2021 after the Premier League received "legally binding assurances" that the Kingdom of Saudi Arabia would not have any control over the club.
The dispute had centred over who would have controlling influence of Newcastle, and would therefore be subject to the league's owners' and directors' test.
Premier League chief executive Richard Masters told the BBC in November 2021 that if his organisation found evidence there was state involvement in the running of Newcastle "we can remove the consortium as owners of the club".
The PIF has declined to comment while Newcastle have been contacted.
