We’ve previously discussed this issue (though not this precise quotation) in
this thread and
this thread (I would, ahem, humbly recommend my posts in those threads

). From one of those posts of mine, I would suggest this as a summation of the issue:In other words, can we prove that one of the Apostles consecrated some bishop, who consecrated some bishop, who consecrated some bishop, … etc. etc. for twenty centuries …, who consecrated the bishop that ordained this particular priest? Unfortunately, we do not have the records to allow us to do this. However, we believe it did happen – that every bishop today was consecrated by somebody, who was consecrated by somebody, who … etc. etc., who was consecrated by one of the Apostles.
Why do we believe it without documentary proof? For two main reasons: (1) the evidence we do have shows that people have always taken the issue of apostolic succession very seriously, so there is no reason to think that they just gave up caring about it for a few of the centuries from which we don’t have records; and (2) because we believe that the Church is divinely instituted and guided by the Holy Spirit (and “the gates of Hell shall not prevail against it”), we believe that God would not have allowed all our bishops and priests to have fallen into invalidity at some point in the distant past.