You are right about any more sounding wrong, but that's because the author attempted to use a standard form but got it wrong. The standard form is:
One cannot do X any more than one can do something impossible.
One cannot become rich on the stock exchange any more than one can get blood from a stone.
In this context, any more has the literal meaning to a greater extent: used in this standard form, it must be followed by than.
The writer made the mistake of changing cannot to can no longer in order to add the concept that it used to be possible but that it isn't any more. It is not clear, though, whether the no longer is intended to apply only to X, or to both X and the impossible activity.
In addition, this confuses the standard form, because no longer seems to be duplicated by the temporal meaning of the expression any more. Note that this meaning does not work with than, so it is definitely not what the author intended.