I think that transubstantiation is an unrelated issue. The original argument is that changes to the form of their episcopal ordinations rendered all of their ordinations invalid.
Worked like this.
Apostolicae Curae found two related objections to the validity of Anglican orders, from the point the supposed invalid form on the Edwardine Ordinal was used. The form of the consecration/ordination rite was judged invalid, due to not mentioning the power of the priesthood to offer the sacrificial Mass. But this was not uncommon, in liturgical rites which the RCC does recognize as validly conveying valid orders, other things being equally valid (
Saepius Officio mentioned this). So the question of valid intent was intertwined with that of the liturgical form.
Valid sacramental intent is, as *Apostolicae Curae * says, an interior condition of the sacramental minister, and not necessarily subject to positive examination or judgment. The minimum required for valid sacramental intent is for the minister to intend
facere quod facit eccelesia, to intend to do what the Church intends, in the action. Since intent is interior, valid intent is normally assumed, if all other aspects of the sacramental action (minister, form, matter, subject) are themselves demonstrably valid. However, if there is some external aspect that permits a judgment of the intent, permitting a
determinatio ex adiunctis, that may permit a judgment of invalid intent. In the logic of Apostolicae Curae, that was the use of the Ordinal. Given the circumstances in which the Ordinal was written, and by whom, it was assumed that the intent of anyone who used that form sacramentally was (by
determinatio ex adiunctis) considered sacramentally invalid. Thus, through the joined questions of form and intent, each leading to a determination of invalidity, the orders were declared invalid. Had the Ordinal not been written, and the
Pontificale Romanum continued in use, the logic of
AC would have been necessarily different. Not that the Orders would have been declared valid, necessarily, but some other point might have served.
The supposed defective form in the Ordinal was cured, in the 1662 revision to the Ordinal, for reasons unrelated to this question. The logic of the Dutch touch, then, would be that the form is now not what it was, and one might logically assume that OC bishops, validly though illicitly consecrated, would convey valid though illicit orders to Anglican bishops, who would transmit them in turn. Logically, that is. I am not aware of any formal, official RC pronouncement on that. But it is quite clear, in the statements of the first OC joint consecrators, that their intent was sacramentally valid.
It is a long, sad story, involving theology, history, politics and personalities. Much of history is like that.
GKC
Anglicanus Catholicus