First off: Saying something along the lines of "sue me" doesn't really increase your chances for a satisfying answer in my experience.

Well, to answer your question if you're still interested: No, he didn't. The salute wasn't always "Heil Hitler" anyway. Although terms like "Nazi salute" or "Hitler salute" (Hitlergruß in German) are widely used now to refer to the act, it was mostly called Deutscher Gruß (which translates as "German salute") and later sometimes Führergruß during the time of National Socialist reign. It was not totally new either as was used in a similar fashion by Italian fascists too (which in turn mimicked a fictionalized "Roman salute"). The salute fits popular mass movements like fascism or National Socialism perfectly well as it gives a "martial vibe" off if performed by crowds at once while also being easy to pull off. Under National Socialism the party tried to supplant common greetings like "good day", "good morning" etc. with the German salute with varying success. (Hard to measure the success. The popularity of the regime surely cannot be measured simply by comparing the number of "Heils" to the number of traditional greetings.) You could also use the salute as a complimentary close to a letter by writing "with German salute" (mit deutschem Gruß) instead of something like "best regards".

While performing the salute you were not necessarily required to say "Heil Hitler", variations included: "Sieg Heil" or simply "Heil". So one could easily reciprocate the salute without using the name. I know it's disappointing but there was no awkward situation where Hitler had to say something like "Heil Myself" in order to salute his subjects.