I direct you to Pope Gregory VII by H.E.J. Cowdrey - the foremost modern expert on Gregory VII in the English speaking world. Please note that Cowdrey is a Protestant clergyman who has no personal sympathy for even the legitimate and documented writings of Gregory VII.
He addresses the question of the authorship of the document we're discussing - he is probably the only person who ever personally went through every single surviving document of Gregory VII's papacy and translated them.
He published all 400 documents as The Register Of Gregory VII and explains how the vast bulk of documents personally attributed to Gregory VII include documents written by officers of the Curia, letters written to Gregory by other people, etc. He demonstrates how dubious the supposed Gregorian authorship of the so-called Dictatus Papae is.
so by your statement above, whose lying? A little louder, please.
The answer: neither I nor Cowdrey.
see post #107