You fail history. Forever.
In the elections on 6th of November, 1932, the NSDAP became the strongest party in the Reichstag, with 33.1 percent of the votes. Chancellor von Papen resigns. Lieutenant General von Schleicher takes the post, and tries (unsuccessfully) to break up the NSDAP.
On January 15, 1933, the Landtagswahl in Lippe is won by the NSDAP with a clear majority. This increases the pressure on the Schleicher Government.
On January 28, 1933, Chancellor Schleicher resigns, because President Hindenburg refuses to accept his plans for a minority government.
On January 30, 1933, Hindenburg asks Hitler to form a new Government.
All of this was perfectly legal. Hitler was in a position to form a new Government because his party was the majority leader in the Reichstag. They were elected. Simple as that.
If you have proof otherwise, please show it to me. Please note that anything AFTER January 30th doesn't really count as democratic anymore. After they had the power, they used it to ensure that they wouldn't lose it again, but that doesn't change the fact that they WERE elected legally.