How can the NO clergy hold office (according to the thesis) if they aren't 'real' clergy?

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Bishops throughout history, and even popes, have been elected or appointed to office prior to receiving episcopal orders (and sometimes without ever receiving episcopal orders-- St. Bonaventure, to name one notable example; Pius III was elected pope while still a deacon and died before receiving even the priesthood never mind episcopal orders).  Spiritual authority (jurisdiction) is meant to go along with holy orders, but is perfectly capable of being possessed and exercised by someone who has not received holy orders.
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In other words, even if the new rites of transmitting holy orders are invalid, this does not pose a problem for the continuity of jurisdiction.  That is what someone who holds the thesis would tell you, and they would be correct in so asserting.
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Now, there might be a debate over whether a man needs to belong to the "clerical state" (which is initiated through the reception of tonsure-- well before any major orders are received) in order to have and exercise jurisdiction.  That is a rather obscure debate and I don't know the answer to its questions. But I tend to think that it probably isn't absolutely necessary for a man to be tonsured in order to receive jurisdiction (although it is, of course, necessary that he be a member of the Catholic Church). I could be wrong.