Intention must be manifest, that is, the intention must be able to be known in the external forum.
A priest, for example, who reads the Mass and performs the rites according to the Missal is manifestly doing has the Church does. His intention is manifested by the actions he is performing. If, on the other hand, the same priest explains his intention in the sermon that he is merely re-enacting the Last Supper and that the bread and wine on the altar is symbolic of Christ's Body and Blood, there would be grave doubts about whether there was a valid Mass.
In the traditional Mass, the intention of the priest is made manifest in the Offertory, so that, even if he internally doubted the Sacrament or positively disbelieved in the Sacrament but never made this known, the Sacrament would still be valid.
In the Novus Ordo, there is no prayer in that service which makes the intention of the priest manifest. Thus, his intention is not manifest and if he believes other than what the Church teaches in regards to the Sacrament, his Masses are, at best, doubtful. Because seminarians in the Novus Ordo are positively taught heresies in many seminaries, the very ability of the Novus Ordo priest to offer a valid Mass is, likewise, doubtful.
At least, this is what Archbishop Lefebvre wrote in his book, Open Letter to Confused Catholics. I recommend that you read this book. While it is not a theological treatise, I think it would answer the questions you seem to be raising better than what I or anyone on CathInfo can explain.