If you mean the case for their existence or non- is settled, I beg to differ. While there has never been a successful tracing of the route (as in running a line from one end to the other), and probably never could be now thanks to dynamiting at several points and the active erosion at depth via the so-called solution channel undermining its course, the 1897 interception of a small rectangular tunnel lined with beach stones from which seawater poured forth at pressure, at approximately 111 feet deep in the Money Pit, is kinda tough to ignore. The classic skeptic argument against is that this was either a searcher tunnel (though its 2.5 foot width and beach stones would tend to work against this theory) or a natural channel (its squared off ceiling would say otherwise ... nature's not that fond of right angles).
Another argument raised is that even if the bed was lined, the sides were not, and natural erosion would have done a number on them over time. This seems likely in a scenario where the water is constantly flowing at force, but once it has flooded a given shaft, the water is calmer and only moving with the tides, so the "waterproof" hard-packed clay till forming the sides of a channel might have resisted erosion for an extended period.
If there were no man-made flood tunnels then the question of what the finger drains were for becomes necessary to answer. The salt-works theory, though well-argued, is still only a theory.
So like everything else on OI, still an open question to those with open minds!
--GT