I know that I have seen on the web an Orthodox lineage that appears just as valid as the Catholic one.
I have a feeling that if I hung around the Eastern forum for a while that the Orthodox might state the issues a little differently.
Under the “visible church” proposition it would seem to me there must be some (Biblical) criteria that points to one and only one denomination.
A separate issue is whether apostolic succession is that criteria. It seems to me that the stronger case is that this is a historic criteria rather than a Biblical one. But that is a separate issue.
Also, in my mind I have always separated two issues:
(1) Whether the church was established as a visible church. I have never used the word visible though, I have thought in terms of whether Jesus established a unified centralized church under a common hierarchy.
(2) How Jesus views His church today.
If the Catholic position on (1) is correct, it does not necessarily follow that the Catholic position on (2) is correct.