There was a mounted charge by two squadrons of the Scots Grey at St Quentin on August 28, 1914 - but it took place after a German attack had already been beaten off by dismounted cavalrymen, so most of the stories about it are indeed propaganda. So it would be correct to say that while a charge took place, it was nothing like it was depicted by the press and in paintings.

Here's what one historian of the British cavalry in the Great War has to say about it:

"This bloodless charge was seized on by the press, and the Illustrated London News printed a Richard Caton-Woodville painting of the event, complete with kilted infantry soldiers of the Black Watch hanging from the stirrups of the cavalry. This recalled an almost certainly apocryphal story of the Scots Greys' charge at Waterloo, where infantrymen were said to have accompanied the charge in this fashion. It almost certainly didn't happen in 1815 and it definitely didn't happen in 1914, as no British infantry were to be found within several miles of the battle. However, the myth stuck and a bronze figure group depicting the same fictional event remains in the collection of the National Army Museum in London."

Source:

Kenyon, David. Horsemen in No Man's Land: British Cavalry & Trench Warfare 1914-1918. Barnsley, Pen & Sword Military, 2011.