Ok. This has been a hobby of mine, online, for many years. I was sure that someone would have filled in the question. But I’ll do it, in spite of my my vow of restraint.
The point is not merely the form. The point is also intent. Sacramental intent, as the other sacramental factors (such as form) must be valid to validly confect the sacrament. The defect in form is noted. But that in itself would not necessarily have rendered the judgement of AC. There are ordination/consecration rites with the same “defect” that the RCC recognizes as valid for ordination/consecration. In this case, the defect of form is coupled with the defect of intention.
The logic is that the writing of the form, as contained in the Edwardine Ordinal, at the point in time it was done, in the theological /political context in which it was done, and considering by whom it was done, the lack of a definitive statement of the the full sacerdotal powers of the sacrament of Holy Orders (that of confecting a valid Eucharist) was judged a deliberate conscious act of theological belief, and that while the preface to the ordinal, and several points in it, refer to the three Orders of ministry, the omission of the reference to the Eucharistic sacrifice, deliberately made, reflected a difference in the meaning of the names of those ministers. A priest in the sense of historic usage was not intended. Something else was being done.
Intent is, as AC says, usually a simple factor to determine, as to validity. Being an internal state, not observable, it is not directly measurable. it’s basic requirement is a sacramental intent to do, in the sacramental action, what the Church does in the action (facere quod facit ecclesia). If all other sacramental factors are valid (form, matter, etc) then the intent is taken as valid also. Absent some other point which permits a look internally, a method of determining by other means (that allow a determinatia ex adiunctis) the validity of sacramental intent). This, in the judgement expressed in AC, is the use of the Edwardine Ordinal, constructed when and by whom it was, constructed, as judged, to deliberately excise the sacerdotal portion of the priest’s role… Hence, the sacramental intent of someone using the Ordinal is judged invalid.
There is a great deal of history, personalities, and politics involved in the long, sad tale of AC. For the point here, the book you want is Clark’s ANGLICAN ORDERS AND DEFECT OF INTENTION. For a really good account of both the history of the story, and a close look at the theological question overall, Hughes’ ABSOLUTELY NULL AND UTTERLY VOID, and STEWARDS OF THE LORD are recommended.
All RCs, regardless of the history, politics, personalities, etc, of the issue, should affirm the judgement of AC, at the appropriate level of theological certainty. Others (say Anglicans of the sort mentioned by the OP) may do otherwise