I can find no evidence on the Internet to support this assertion. The closest I can get is the Daily Telegraph's obituary to Prince Rainier, according to which "In 1962 ... Prince Rainier relaxed his ban on her appearing in films to the extent of giving her permission to appear in Alfred Hitchcock's Marnie. But she had to withdraw when it became clear that the Monégasques recoiled from the idea." There is no mention of a ban on her films being shown; but the final comment in the section I've quoted would appear to suggest that the locals didn't want to watch them anyway.
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