In German, the letter Z is pronounced "tset". The "t" is not silent, but inflected.
"Nazi" is thereby pronounced "nah-tsee" -- which sounds very close to "naht-see".
I've heard dozens of Germans pronounce it with a soft “s.”
I've never heard it pronounced “tset” with an inflected “t.”
My own German is very basic, so I can't dispute what you say.
But I am surprised to hear all this.
By the way, at least one native born German thought that “zi” comes from Sozialist, which is where I got the idea.