Rutherford didn't really "piss off Hitler".
Hitler hated, and had nothing but contempt, for the Bible Students. Hitler had fought in the First World War and expressed his dislike of the evangelical soldiers who served on the front lines. He blamed them for reducing morale on the front lines. He speaks of this in Mein Kampf.
Something that few JWs know is that the Bible Students in Germany donned the German uniform in WW1 - the German Watchtowers listed the Bible Students who served, and those who died, defending Germany. At the same time, the Watchtowers from other countries extolled the virtues of the Bible Students who refused to serve their countries.
In 1925, Rutherford had a huge falling out with the German WT branch, resulting in Conrad Binkele splitting form the WTS, and taking a large number of German Bible Students with him. The German WT saw a great chism happen with few left to follow Rutherford's 'new' theology. (more about that later...)
At the same time, trouble was brewing on American soil and the same thing happened - about 75% of the Bible Students left the WTS.
And...another thing happened in 1925 - Hitler wrote Mein Kampf - the sales of which went to finance his new political party - the National Socialist Party. The book - Mein Kampf - was purported to have been read by anyone and everyone who had interest in world politics - many copies were given away to world leaders and people in politics.
I have no doubt that Rutherford and others in the WTS read Mein Kampf. Their entire religion was based on political events and world conditions.
Back to 1925 - it was around this time - the years between 1925 and 1931 - that Rutherford made a radical change in the WT doctrine. Very radical. Rutherford changed the doctrine that Russell had vigorously espoused for all the years he was the figurehead - the Zionist doctrine. Russell fully supported the return of the Jews to Palestine. It was an integral part of his theology.
So, by the time that 1931 rolled around, the WT religion needed a new name - it was a very different doctrine that Rutherford introduced - replacement theology. The articles published in the WT that supported the Jews returning to Palestine were now replaced with the promise of the New Jerusalem being realized out in California - in Beth Sarim, the mansion that Rutherford built with the support of the Coca-Cola Heath family.
In 1933, when Germany seized the printing presses of the German WT, Rutherford believed he had a solid case to make to Hitler to get the WT property returned (under conditions of the Versailles treaty that allowed American corporations to operate in Germany). The case he made in the letter to Hitler was based upon the assertion that the WT no longer was the same as the Bible Students - and it wasn't the same.
The stories and events that have been recorded about the JWs in WW2 are conflicting - and that is because the religion of the WT was split - there were many of the 'old' Bible Students who still supported Russell's Zionist doctrine imprisoned along with the 'new' JWs who did not support Zionism. The work camps became the place where this 'sifting' occurred. Along with the accounts of Bible Students being killed and tortured, are the accounts of the JWs who received special privileges from Himmler's SS.
By the time the war ended in 1945, Himmler had made arrangements to release the JWs sent on work assignments with just a handshake - they didn't have to sign a declaration denouncing their religion. The JWs who took these privileged positions with the SS were considered 'partially free'.
Himmler's plans for after the war included using the JWs as a vanguard in areas that Germany would have control. Himmler had great admiration for the JWs loyalty - the same quality that he held his SS troops to.
Some researchers have pointed to 1942 as the date that the JWs started to be treated better in the work camps. There are various reason given as to why this occurred, but what is left out of the narrative is that Rutherford died in 1942. It was Knorr who was in charge of the WT when this apparent shift in treatment occurred.