Ultimately this is really a terminology question, that gets a lot of nationalist baggage.

Auschwitz was located in the area that Germany annexed, not the "General-Goverment" that was German-controlled but nominally not Germany. So from the perspective of Germany, it was in Germany.

But no one besides the German government really recognized this annexation. I sincerely doubt Poles in the area at the time would've agreed that they were in Germany. They weren't German citizens. Further, it's often useful to place things geographically in what country they're in now, which certainly would be Poland. It was Poland before the war, it was Poland after the war, it was only Germany through a legal fiction during the war.

But as you said, it was obviously run by Germans. Many of the camps had a substantial number of non-German collaborators there too, but I don't know whether that was the case in Auschwitz. Generally when I've heard of that the collaborators were Ukrainian, not Polish.

This question gets wrapped up in nationalistic issues because a lot of Polish people, for understandable reasons, want to avoid the implication that Poland/the Polish people were involved in the Holocaust. This results in controversy when people refer to the Death Camps as "Polish". But the fact that people get squirrely about the terminology does not change the reality that Auschwitz was/is located in Poland, along with a lot of other German genocide infrastructure.