It is true that U-203 sighted Texas and stalked her for several hours in June 1941. The submarine was unable to obtain a firing solution and did not engage the battleship. It is not true that the submarine had orders to attack American warships.

Germany still sought to keep the United States neutral at this time. Quoting from Michael Gannon's Operation Drumbeat:

Thus, ever since the previous June, when Germany invaded the Soviet Union (Operation Barbarossa) expecting to conquer the Russian defenders with a series of Blitzfeldzuge (lightning campaigns), Hitler had assiduously avoided any incident that might provoke U.S. entry into the war at that particular time; though from other evidence it is clear that he intended to make war on the United States after other, more immediate targets had been seized or neutralized. That caution was expressed on the very eve of the eastward plunge by Donitz's superior, Grossadmiral Raeder: "Until the effects of Barbarossa can be seen, that is, for several weeks, the Fuhrer wants every possible incident with the U.S.A. to be strictly avoided." As events transpired that caution had to be observed for months instead of weeks. On 9 July, anticipating victory in the east no sooner than September, Hitler told Raeder: "It is vitally important to put off America's entry into the war. ... There must be no incidents with the U.S.A. before mid-October."

However, it could have happened anyway. The first American ship sunk by German U-boats was the merchant ship SS Robin Moor in May 1941, before the U-203 found Texas. The Robin Moor was clearly marked as an American ship with U.S.A. painted along the side of her hull and torpedoed on her beam by U-69 during daylight, meaning her attacker must have seen her markings. The captain of U-69 was not removed from command despite this.

Gannon briefly discusses U-203's encounter with Texas later in Operation Drumbeat. This excerpt refers to the German U-boat command (Befehlshaber der Unterseeboote, or BdU) and the destroyers for bases deal between the United States and Great Britain in 1940, which included the United States transferring 50 out-of-use destroyers to the Royal Navy.

On 20 June, though the incident was not known until after the war, U-203, commanded by Kptlt. Rolf Mutzelburg, attempted to attack U.S. battleship Texas in the Western Approaches to Britain. After a sixteen-hour pursuit U-203 was not able to overtake Texas and obtain a favorable attack position. There is no record to show that Mutzelburg, either, was held to account for violating the Fuhrer's strict directive against "incidents," and Donitz seems to have accepted his commander's explanation that he thought the battleship, like the fifty destroyers, had been transferred to the British - a suspicion lent some credence from the fact that Texas was east of the Pan-American Security Zone and inside the announced German operational area surrounding the British isles. Donitz issued new orders to all boats: "U.S.A. warships should not be attacked even in the blockade area, since the present [BdU] permission to do this does not seem to agree with the political views of the Fuhrer." Fearing that boat commanders might mistake a U.S. destroyer for one of the fifty former U.S. destroyers exchanged to Britain, on 21 June Hitler required BdU to signal all boats that "Attacks on warships within and outside the blockade area" must until further notice be limited to "cruisers, battleships and aircraft carriers and only if these are definitely recognized as enemy [excluding U.S.] vessels."