The statement is pretty much nonsense with little basis in fact. First off, it assumes that the British and American business interests were the motive force behind Hitler's seizure of power which assumes that both countries' economic leaders had significant sway within the German political system. Although both Britain and the US were very important trading partners to interwar Germany, the strength of foreign investment did not translate into Anglo-American firms having their way inside Germany itself.

Indeed, the notion that non-German firms had the ability to stack the political deck in Germany in their favor would have struck many Anglo-American businessmen of the era as absurd given the many difficulties they had operating within Germany. GM's acquisition of Opel in the 1920s provoked a considerable response in both the German press and government over foreign takeovers of German industry and Opel had to operate under a strict regimen of oversight so that it did not harm the wider German economy. The National Socialist state added a further layer of state interference and control to foreign-owned subsidiaries. Management of these entities like Opel often now had to be German-run and subject to Hitler's drive for both national autarky and rearmament. The latter meant that industrial lines had to be retooled and standardized for a shift over from military production. Both profits and dividends of German firms could no longer by law be remitted back to the US or UK, and Anglo-American companies often delegated control to their subsidiaries. The oft-heard claim that companies like Ford or IBM thus profited from the Holocaust and German aggression often overlook this salient detail. In many cases, these companies were de facto German companies run inside Germany by Germans and worked much more closely with the German government than their parent companies.

Moreover, the economic policies pursued by Hitler were often quite contrary to the wider interests of the Anglo-American business world. Autarky meant that the Third Reich was primarily interested in gaining minerals and other commodities from abroad instead of finished goods or other high-profit items. German trade missions to Latin America and Eats Asia sought to gain commodities like tungsten that would further aid rearmament. Although the Third Reich's government begrudgingly tolerated the existence of foreign-owned firms like Opel or allowed companies like Standard Oil to modernize IG Farben's plants, the state clearly favored the development of German firms like Mercedes Benz and its rhetoric clearly stated this priority. This fusion of autarky and nationalism was contrary to principles of free trade and explicitly ruled out any constructive partnership between German industry and Anglo-American capital over the long term; in Hitler's Weltanschauung, German industry should never accept any true rivals. Hitler's reckless drive for rearmament actually came close to overheating the German economy in 1938 and had war not intervened, it was likely that the German economy would have collapsed, which underscores again, Hitler's policies were often not in the wider interests of Anglo-American capital, nor was they funding Germany's rearmament.

While there was some ideological congruence between the Third Reich and various financial leaders, especially over the Third Reich dispensing of labor laws, the harnessing of patriotic sentiments of Germany, and the elimination of the Communist Party (KPD) as a political threat, this did not translate into a wholesale acceptance of the Third Reich or its program. Even Henry Ford's antisemitism and sympathies for Germany during World War I did not really garner Ford-Werke a favorable position within the Third Reich's economy. While some Anglo-American business leaders welcomed Hitler's promise to restore order after the chaotic years of 1929-33, they tended to have a bad time operating inside the new order. The Third Reich's economic system favored cartels and monopolies of German-held firms, and foreign businesses operating inside Germany became increasingly anomalous. While Anglo-American firms have been less than forthcoming about their activities inside the Third Reich and the nature of their financial dealings with Germany, they were far from a motive force within Nazi Germany.

The notion though that the Third Reich was a proxy for capital though was paradigm that has its origins in the USSR and it served several political purposes. Firstly, it explained the failure of the KPD to gain traction within Germany during the Depression and the suddenness of its collapse after Hitler's seizure of power. The Depression was seemingly the ideal moment for the proletariat to mobilize and complete the work of 1917, but despite increased activism by the KPD, an alarming number of the German working classes who drifted over to the NSDAP in elections between 1929-33. The idea of a nefarious plot by capital to denude the working classes of their revolutionary energies was a more comfortable narrative than the idea that some elements of the NSDAP's program were attractive to the German working class and that the KPD had squandered its political opportunities. Such a picture fit into a preexisting narrative explaining the rise of Fascism in Italy as a plot by capital to keep the working classes chained via nationalism and militarist expansion. This narrative found new life during the Cold War in which Soviet propagandists sought to connect the US with Hitler and portray the Western Allies as less than serious partners in the destruction of the Third Reich.

A Google search of "Nazi Germany was fomented by American and British capitalism as a proxy with which to vanquish the Soviet Union" reveals that the phrase was used in a news piece from Sputnik News, a state-affiliated news source that some commentators in the West have found less than reputable- see here, here, ad here. In this case, the idea of a Hitler as a proxy of capital is a leftover of Cold War propaganda, which like many leftovers, it is a smarter idea to throw them away than to consume them.