> The Nazis had strong support. But Hitler was appointed.

Well, yeah, PM’s (and the Chancellor in the German system at the time, and now, is a PM) are almost invariably appointed by the head of state after either a general election—or sometimes between them if an incumbent resigns or a vacancy occurs by other means—as the leader of the majority party (if any), the leader of the majority coalition (if there's no majority party but there is a majority coalition), or sometimes (and whether this is allowed and whether it makes a sooner next election than would otherwise be required varies) some minority party leader based on some combination of size of minority, support and opposition from other parties, and discretion of the head of state.

And, yes, Hitler was first appointed as the last and weakest kind, but that's still effectively winning the tiebreaker set out for an ambiguous electoral result, since it could only happen because no other party or coalition could form a legislative majority.