Ray
Hitler came to power because the Nazi Party had more seats in government than another party and In January 1933, Hitler became Chancellor (the German President/Prime Minister) when he became leader of the Nazi Party.
This is identical to the UK today. Tony Blair was leader when Labour attained more seats in government than any other party. He retired and Gordon Brown is now Prime Minister. There need be no new election to change leader.
As for wikipedia - it is frequently misleading and some times ridiculously wrong. Here, however, you have been mislead by European government terminology. Hindenburg was not in control and was reluctant to lose power, but his party were losing confidence in him. He tried to unify the party, frst via Papin and then by Hitler. As wikipedia has stated the President "reluctantly agreed to appoint Hitler". In Germany, it is the duty of the President to anoint the political leader, not his choice and to have refused would have led to another election, or the President being overruled by Reichstag vote. In the UK, the Queen holds the same responsibility and calls the leader of the majority party to Buckingham Palace, where she commands him/her to go away and form a government.
This is often an easy process, where one party has a majority, but just as in the Israeli elections recently, it is not always so. Netanyahu was asked to form a coalition government, although a different party had won more seats. This was because it was thought he would be able to pull together a coalition better than the opposition.
Perhaps you should use better sources, read into the background and read whole articles before commenting.