Cantarella, this is the dogma as quoted directly from V1:
Wherefore, by divine and catholic faith all those things are to be believed, which are contained in the word of God as found in scripture and tradition, and which are proposed by the church as matters to be believed as divinely revealed, whether by her solemn judgment or in her ordinary and universal magisterium.
This is that same dogma, only in this quote, I replaced the words
"in her ordinary and universal magisterium", with Pope Pius IX's explanation of what the ordinary and universal magisterium is, as he taught it from Tuas Libenter. The dogma's meaning has not been changed.
Wherefore, by divine and catholic faith all those things are to be believed, which are contained in the word of God as found in scripture and tradition, and which are proposed by the church as matters to be believed as divinely revealed, whether by her solemn judgment or "all that has been handed down as divinely revealed by the ordinary teaching authority of the entire Church spread over the whole world. (...and which, for this reason, Catholic theologians, with a universal and constant consent, regard as being of the faith.")
The only commonality the true dogma has with the false NO doctrine you keep referencing, are the words, "spread over the whole world".
In the false NO doctrine you constantly reference as if it is a true teaching of the Church, it is the bishops who are infallible - whether spread over the whole world, or not, just as long as they're in union with the pope. Again, this is a false teaching, do not believe it! - and this false teaching has proven to be the cause of the loss of faith of billions.
In the true dogma, it is the teachings that are infallible, provided those teachings have been taught by the Church always and everywhere. This is the same as saying: "in her ordinary and universal magisterium."