How do you know the zimmerman note was a reliable source

The Zimmermann Note was first suspected of being a forgery by the British, to make the Americans think that Germany wanted to cause war for the USA, and thus pushing the Americans to help the British. However, while the USA government officials were still debating whether this was a genuine note, the German Foreign Secretary, Arthur Zimmermann himself, admitted the note was genuine.

There would have been no reason for Zimmermann to falsely claim that this note was true, as this admission would have caused America to indeed join the war against the Germans.