Still, this gives proof to the lie that Vatican II did away with the Latin liturgy.
It's not a lie. The very same passage that talks about giving pride of place to Gregorian chant can also be used justify practically any music. Earlier in the same document, there is permission to use more vernacular in the liturgy at the discretion of the bishops. It did not say that Latin must be removed but nevertheless made it possible for vernacular to become the norm.
The Vatican II documents are open to widely different interpretations. I suspect that many, maybe most, of the Council Fathers who signed them believed they were agreeing to something orthodox. They could not have foreseen what happened.
There was something called "the Spirit of Vatican II" which was a widespread movement to interpret and implement the documents in the most liberal way possible, even to the point of heresy. This "Spirit" dominated the Church hierarchy in the decades immediately after the Council, even more than it does now. (Although Francis has been changing that.)
This, by the way, is the historical context of the founding of the SSPX in which one must understand the actions of Archbishop Lefebvre. When I encounter the sort of people who claim he was schismatic, I sometimes try to explain this background to them.