There’s also a relationship between the phrase 'People of God' and another conciliar phrase, 'Sense of the Faithful' (sensus fidelium). Taken out of context, both terms can lend themselves to the utterly false notion of internal polls defining magisterial teaching. In the sense that the Council used them, both terms presuppose 'thinking with the Church.'
You're right. And I've noticed from many of these threads that there is a reflexive defense of treating the definition of magisterial teaching in such a way. No one ever calls it polling or would admit to such an influence, instead they call it Living, much as those who call our Constitution living, with the same, predictable results. I think that's what is most worrisome: traditional catholics who state that even if the Magisterium teaches against what it has always taught, right is right, and wrong is right. They pledge allegiance to both fallibility and infalliblity.