That's not entirely inaccurate. Churchill got cold feet about Overlord and feared it would be either a slaughter on the beaches or would end up in a WW1 type stalemate.Just watched "Churchill" with Brian Cox taking on the eponymous role.
I think he got Churchill down to a T but the writers seem to have had an 'agenda' in their writing. Painting Churchill as a doom sayer trying to get Overlord cancelled. Churchill was certainly a meddler and not shy in sticking in his oar but I don't think he would have been working to undermine Overlord quite as much as is shown.
There's a record in someone's diary (I think Alan Brooke, CIGS) that WSC proposed an alternative plan shortly before D-Day, an assault on the European 'soft underbelly' via Italy &/or South of France. The planning staff were diverted into investigating this alternative plan and presenting the findings to WSC. The General then told Churchill bluntly that he'd wasted everyone's time with his proposals, that they'd better things to do, that Overlord was the product of years of planning and preparation by the best strategists in the UK & US and the best thing he could do now would be to butt out and let them get on with their jobs (or words to that effect).
"When Churchill's many fanciful strategic ideas collided with sound military strategy it was only Brooke on the Chiefs of Staff Committee who was able to stand up to the Prime Minister. Churchill said about Brooke: "When I thump the table and push my face towards him what does he do? Thumps the table harder and glares back at me. I know these Brookes – stiff-necked Ulstermen and there's no one worse to deal with than that!". It has been claimed that part of Churchill's greatness was that he appointed Brooke as CIGS and kept him for the whole war".
Churchill had done similar things in WW1, his Dardanelles campaign was intended to sidestep the entrenched stalemate in Flanders and he'd had some role in financing the development of tanks/landships, whilst First Lord of the Admiralty. There was a Royal Navy infantry division in Flanders, so it wasn't completely outside his remit.
"...And the wonderful thing is that 3/4 of the population of the world imagine that Churchill is one of the Strategists of History, a second Marlborough, and the other 1/4 have no idea what a public menace he is and has been throughout this war! It is far better that the world should never know, and never suspect the feet of clay of this otherwise superhuman being. Without him England was lost for a certainty, with him England has been on the verge of disaster time and again.... Never have I admired and despised a man simultaneously to the same extent. Never have such opposite extremes been combined in the same human being."