The timeline you mentioned is somewhat off, but the story itself is true. Hitler saw the prototype on November 26. 1943. He asked if the plane could be fitted with bombs. When the company answered yes, Hitler agreed on the production if the design was turned into a "Blitzbomber".

Numerous people within the Luftwaffe disagreed and tried to persuade Hitler to use the plane as a fighter, but it took until early 1945 until the Me 262 was used in the role it had been designed for. And while it was very dangerous as an interceptor, there were too few to have a real impact on the war. The main advantages were the high speed, which allowed the Me 262 to outrun escort fighters and the heavy armament.

Why did Hitler act this way? First, Hitler in 1944 was not a very stable person. The strain of commanding the german army for years had taken its toll, and he was abusing a lot of medical products. According the statements by people in his vicinity, he was prone to fits of rage and depression and was very capable of acting irrational. Many people have classified him as clinically insane by this point.

While the actual motivations will remain unknown, german-language sources claim that Hitler had a large desire for revenge against the western Allies. He hoped that the Me 262 would be able to bomb England and the allied forces with impunity - even though the payload was low and the design was not optimised for bombing runs.

The story of the Me-262's use as a bomber is somewhat convoluted and exaggerated in postwar memoirists such as Adolf Galland. In February 1943, a Führerbefehl decreed that all fighter aircraft should provision for bomb racks so they could be used as fighter-bombers. Willy Messerschmitt then incorporated the provision for bomb racks into the design and began development on paper for pure bomber variants of the 262. In September 1943, Messerschmitt personally assured Hitler that the 262 could be used as a high-speed bomber over southern England. When Hitler saw a 262 on display, he inquired whether it could carry bombs and Messerschmitt again affirmed that the 262 could carry a decent bomb load. From all this, Hitler got the impression that the 262 was analogous to the Ar234, a bomber that would use speed to evade enemy defenses. By January 1944, at a conference with Milch and Speer, Hitler stressed that the bomb load of the 262 should be increased, so when a Jagerstab conference on aircraft production the following May noted that the 262 was to be a fighter, Hitler thought his orders were being deliberately flaunted. Milch tried to argue the case for the 262 as a fighter, but Hitler would have none of it. Goering subsequently sent out a directive stating, "The Führer has ordered that the Me 262 is to be operated purely as a high-speed bomber. There is to be no mention of it as a fighter until further notice."

So, what impact did this have on the deployment of the 262? Not very much. The bomber variants of the 262 were already in development long before the May 1944 Jagerstab conference. The 262 program, like many high-technology programs, was beset by technical issues which were compounded by Germany's shortages of strategic materials. The greatest problem for the 262 was what made it so revolutionary: its engines. The Junkers Jumo 004, selected for the 262 after its intended powerplant, the BMW 003 fell hopelessly behind schedule, was a persnickety design and ersatz materials gave it a very short design life. The bugs within the engine were difficult to iron out and prevented any full-scale deployment of the 262 in early 1944. Furthermore, a shortage of trained workers and the pressures of dispersal of factories caused by Allied bombing put a ceiling on how many 262s could be produced.

The 262 as bomber entered into postwar memory as an example of Hitler's strategic myopia. Postwar Luftwaffe veterans would argue that but for the Führer, the 262 could have entered into production earlier and turned the tide of the air war. Writers such as Ambrose uncritically repeated this line was but the reality was the 262 arguably went into service as early as it could have given the circumstances. Luftwaffe pilots also had great difficulty coming up with new tactics and formations which to use the 262 effectively. The convoluted nature of the 262's bomber interlude does indict the Third Reich on a different set of charges. The polycratic nature of the Third Reich, where there were multiple centers of power all dependent upon Hitler's approval, meant that German officials were inclined to try and court the Führer's opinion. Messerschmitt, like many other technical experts in the aviation industry, often misled or exaggerated aviation developments to suit Hitler's expectations. In the example of the 262, Willy Messerschmitt conflated paper projects for a pure 262 bomber with the emerging new design which just had bomb racks.

Sources

Boyne, Walter J. Messerschmitt Me 262: Arrow to the Future. Atglen, PA: Schiffer Pub, 1994.

Forsyth, Robert, and Eddie J. Creek. Me 262 Bomber and Reconnaissance Units. Oxford: Osprey Pub, 2012.

Uziel, Daniel. Arming the Luftwaffe: The German Aviation Industry in World War II. Jefferson, N.C.: McFarland & Company, 2012.