Conclusions from the paper.
The finally line in the article should actually be read first as it clearly spells out where the paper fits in the scientific literature.
So, if re-creating a fold by ordered assembly of sections of sequences
that already adopt that fold is not a simple matter, generating new
folds from parts of old ones may be much less feasible than has been
A popular hypothesis at the time was that some folds emerged at some point or another from substantially different folds.
This paper used advanced statistical analysis (well, they're convoluted, not particularly advanced...) using a very simplified and uncertain model to show that the chimera theory of fold genesis is unlikely. It is a critique of that model at the time, and does not seek to show how long it took for evolution to come up with the fold.
This is an incredibly important question to answer. This paper was probably accepted because it shows a genuine attempt to quantify the probability of a general hypothesis. However, almost every step of their method introduces over-simplification, arbitrary thresholds, and convolution of the biology. As I see it, the only thing the paper can say for certain is "that in a small subset of simple folds, with a tonne of caveats and conditions, it might be less likely than other people think that the fold formed that way".
What your friend is drawing from this.
It would be incredibly difficult, many philosophers would argue impossible, to prove how folds were formed. But to build up lots of different scientific hypothesis and disprove them as much as possible is more achievable. That, broadly speaking, is the scientific method and this paper generally adheres to that line of thought.
This paper is saying "The current hypothesis surely can't be the right method! Look how improbable it is." and your friend has drawn from it "A scientist said more time would be needed, which proves evolution needed longer than it had". A simple misunderstanding; a scientist said a model had problems, a layman thought this meant the problems were the truth. The paper is not aiming to prove anything (The author may be especially careful about doing this given his close ties to intelligent design movements), but I think your friend might be incorrectly using the paper to prove something!