Can estimating the likelihood of protein sequences adopting functional enzyme folds show life is too complex for evolutionary timescales?
I think your acquaintance is trying to fit real science to some of his personal beliefs (that are obviously wrong). 

If you read the article you'll see that it's not about evolution at all, but about protein folding and what proportion of possible sequences gives a working protein. It turns out random sequences are not that likely to fold, which leads to some conclusions about the probable mutational pathways to folded proteins. 

The argument of your friend is sort of analogous to the infinite random monkey theorem. If you put a monkey behind a typewriter and wait long enough, eventually he'll write the complete works of Shakespeare. This doesn't mean we waited billions of years for this monkey to type it up, because the world doesn't work like that. There was just a guy with a brain. 

In case of the proteins, evolution doesn't work by generating newly (random) 300 residue proteins that work 1 time in a billion. Probably in one generation a copy of the protein is made with the same function, and during many generations the function of this protein drifts towards a new function, while all the intermediate proteins stay folded because they're not that different.