I used to know a gentleman in my church who had been a tank driver in the North Africa campaign.
He said that everybody knew it was a lie even then.
On the History Channel WW2 forum, there was long ago a thread posted called “Patton and the Pershing Tank.” It was based on a book or article I’ve admittedly never read. The premise is that the Pershing tank, which was equal in speed, firepower and armor protection to all but the King Tiger, was ready for full production in late 1943, and could have equipped several American units by D-Day. However, several generals, of whom Patton was most prominent, killed the production.
Patton was considered the father of American armor doctrine, and his view was that tank-killing was the province of the tank destroyer (M10 Woloverine and later M36 Slugger). American tanks were meant to be like armored cavalry; intended to exploit breakthroughs rather than create them, intended to shoot up rear areas rather than fight enemy tanks.
Other logistical reasons were advanced for why Pershing production was tabled. One was that they didn’t want to diminish Sherman production while plants re-tooled. Another was that Pershings were too large and heavy for existing bridging equipment.
I don’t know whether the article was true or not. If the premise is true, there are a lot of dead American tankers who might not be had they been given something like the Pershing to fight with.
It is pretty clear that compared to the German and Soviet tanks, until the Pershing came along our tanks were pretty lame.