Not really, no.
I mean, that is a god awful take on the history. That Montgomery was a pompous jackass is neither here nor there, he and all his counterparts were vain egotists (well, the successful ones were). In a time of ruthless all out war, it's really only the personality type that could make it at the top. He was never indecisive though. Montgomery's plan in Normandy once his forces were ashore (and as the critical architect of history's largest amphibious landing, it's hard to point to incompetence) was for the US forces in the west to expand and get first Cherbourg and the Britany ports, while the British army took control of Caen and the lateral road network and engage the bulk of the German army to prevent it interfering with the US army in the west. That was the correct division of labour, logistically and militarily.
The British army was by this stage of the war entirely crippled by manpower shortage, and replacements would no longer keep pace with losses after about July. It therefore made sense for the British to engage the Germans on terms that allowed them to dominate without having to take geographical objectives that would've meant continuing offensives even as the casualties mounted up. Montgomery's plan, to pull the Germans onto the British in the East and allowing the US to expand in the west was the key point in all the pre-Overlord briefings. He had intended to do it around Falaise after taking Caen, but the German resistance around Caen prevented such an expansion. Montgomery probably could've forced his way into Caen earlier than he did, and it might have been better for his own reputation if he had, but his over riding priority was to avoid breaking the British army. The plan worked as well, by the time Bradley was ready to push south of Carentan, two thirds of the German armour was in the East south of Caen, and only a brittle crust south of his own troops that quickly collapsed. It should be noted that this was Bradley's second attempt to break out of the bocage country, and his failure at the first attempt forced Montgomery to ask Dempsey to undertake another offensive around Caen to keep the Germans locked in the East: The ever controversial Goodwood offensive, a poor plan that nevertheless allowed the British to avoid infantry casualties.
Bradley wasn't Montgomery's counterpart, he was, at least for the Normandy battle, his subordinate. Even after he became venomously bitter to Montgomery after the latter humiliated him over the Ardennes he maintained that Montgomery's plan in Normandy had worked. The whole US army saved everyone's bacon when the British failed at Caen narrative was largely an invention from several very pissed off authors, including Bradely's former intelligence officer, that bore no resemblance to the primary sources. Even Eisenhower - Montgomery's superior and Supreme Allied Commander, long after Montgomery had pushed their relationship long past breaking point admitted that "It was his kind of battle, whatever else they say about him, he got us there".