> Both the article and your comment assume that the only mode of interaction for natural language is a very high level description of programmer intent.

No, the article explicitly says that the difference is formal vs informal language.

> Programming remained the use of a formal symbolism and, as such, continued to require the care and accuracy required before.

One can define an operational semantics for (at least a subset of) the programming language (even for sloppy one, since they are still very small and restricted). One can prove the semantics preservation theorem formally, or reason somewhat in a similar way informally.

With natural language you kinda lose it, and we don't even touch the fact that models are probabilistic.