I hadn't heard Catholics say Matthew Parker's lineage was false. He was consecrated Archbishop of Canterbury by Bishop William Barlow of Chichester in 1559. William Barlow had been consecrated Bishop of St David's by Archbishop of Canterbury Thomas Cranmer in 1536.
The usual line of reasoning I've heard is that the Anglican Succession was broken when Oliver Cromwell overthrew Charles I and ousted the bishops. Fortunately for the Anglicans, the Restoration occurred in time for them to be restored and continue the succession. The ECUSA lineage goes through Scotland and ties into the Church of England before Cromwell, thus avoiding that problem altogether.
It's my understanding that PNCC and Old Catholic bishops are the ones who refused to recognize the Pope as infallible after Vat-1. They were summarrily ex-communicated. Wouldn't a hard-core Catholic hold that their succession is therefore null and void?
This is the essence of the Bull "Apostolicae Curae". Parker was "consecrated" using the Edwardine Ordinal, which the Holy See had adjudged in 1555 as being an improper form. By using an improper form after the Holy See had already corrected the English on previous use of it, the "consecrators" manifested a defect of intention as well, since had they intended to create a Catholic Bishop, they could have used the approved form in common use in England prior to 1549, and again during the reign of Queen Mary. That they chose not to was primae facie evidence that their sacramental intention was being guided not by intending to do what the Church does, but by their heretical beliefs about Holy Orders, the Mass, and the Priesthood.
It's my understanding that PNCC and Old Catholic bishops are the ones who refused to recognize the Pope as infallible after Vat-1. They were summarrily ex-communicated.
That accurately describes the Old Catholic Church of Germany, Austria, and Switzerland, which after Vatican I made common cause with the Jansenist/Gallican schismatic diocese of Utrecht in the Netherlands. The Polish National Catholic Church is an American schism resulting from persecution of Polish Catholics around 1900 by the dominant Irish Catholics. Similar ill will towards the "strange" traditions of the Ukranian and Ruthenian Catholics caused the creation of the Ruthenian Orthodox Church in union with Constantinople and Moscow, and the reunion of many Ukranians with the Russian Orthodox.
The Old Catholics and PNCC hold to the Catholic teaching on the priesthood, and have retained the Catholic form of the sacrament of Holy Orders. Therefore, their ordinations are presumed valid.
Wouldn't a hard-core Catholic hold that their succession is therefore null and void?
Yes and no.
Yes, they do have a valid sacramental succession coming down from the Apostles. No, they do not have Apostolic Succession proper, because being cleaved from the Church by heresy, they no longer share the faith of the Apostles. It is an extremely mechanistic view which limits Apostolic Succession to the mere chain of valid Bishops laying on hands.