Modified from an earlier answer of mine

While the platform of the H-1 looks similar to other single seat radial aircraft of its generation, this is more of a function of a shared set of problems often necessitates a similar set of solutions. Hughes, who was a figure with a very large ego, claimed postwar that the Japanese stole elements of his design and other commentators claimed that Japanese envoys had been allowed to examine the H-1. These claims of Japanese inspection are unsubstantiated.

There really is not much substance to this claim as the A6M and the Hughes H-1 represented different design philosophies. The Hughes racer emphasized speed and engine power, whereas Horikoshi's A6M prioritized maneuverability and long range. Later models of the A6M had trouble reconciling demands for more speed as the airframe was so light and could not handle the newer generations of engines very well. The Hughes design was notable for using a radial engine and flush riveting, two design features that the Zero utilized, but this was much less copying by the Japanese and more reflective of a generalized developments in aviation technology of which Mitsubishi was a participant. The Japanese design also incorporated design elements that were more advanced than those of the US. The Japanese were ahead of the curve to an extent was their use of something similar to 7075 aluminum in aircraft construction. The Japanese had developed this alloy in secret in 1936 and bonded aluminum with zinc and chrome to make an aluminum that was much stronger and lighter than other aluminum alloys used by other air forces. They used this alloy for the main spar of the A6M and other aircraft, typically the heaviest part of an aircraft. 7075 came with a variety of tradeoffs; it was more prone to corrosion over time and much more brittle than other aluminum alloys. This is part of the reason why so few Japanese warbirds can be restored to flying condition, their main spar is too corroded to be safe. 7075 only came into widespread use in the US after the Second World War.

A better claim for an aircraft influencing the Japanese was the Vought V-141 of which the Japanese had acquired a copy in 1937. However, a lot of the resemblances are superficial and again represent more of a general trend in aviation technology than technical plagiarism. A good many of the developments of the A6M evolved out of the successful A5M design, as well as incorporating frontline experience from the Sino-Japanese War.

The notion that Japan copied or stole its successful designs stemmed from deep-rooted wartime notions that Japan was simply incapable of producing something that matched Western designs. Claims that Focke-Wulf and Kurt Tank based their FW-190 are nowhere near as plentiful as claims that Mitsubishi stole their designs. This denigration is not just limited to aviation designs. For example, Hector Bywater's 1925 war novel The Great Pacific War featured a Japanese aerial attack on Pearl Harbor. This has entered into popular discourse, especially among Pearl Harbor conspiracy partisans, that the genesis of Pearl Harbor came from this novel. Much of this is tinged with racism as it makes the implicit assumption that Japan was not capable of being as innovative as the West.

Sources

Mikesh, Robert C. Zero. Osceola, WI: Motorbooks International, 1994.

Peattie, Mark R. Sunburst: The Rise of the Japanese Naval Air Power, 1909-1941. Annapolis, Md: Naval Institute Press, 2001.

It seems the only similarity with them is the radial engine and wings at the bottom of the fuselage, but that doesn't seem to be enough to warrant a "they copied us"