It’s a remarkably insular and US-centric view to believe that that story was the reason the United Nations Security Council voted to eject Iraq from Kuwait. It was a piece of propaganda that merely had some air play in the US and which, while it may have been convenient to the US and Kuwaiti governments for the support of the US population, was not the strategic reason for any of the nations involved.
Fortunately we have plenty of primary sources to validate this, from the minutes of UNSC minutes to statements by various heads of government at the time. All make it clear that the war was authorised because Iraq’s invasion of Kuwait was not only blatantly illegal but destructive to the international system. That story didn’t form any part their rationale.