I always thought of natural language as a lossy compression algorithm for ideas, and as always in every lossy compression, you sacrifice some accuracy for the sake of brevity.
To an extent, sure, but he didn't say "unambiguous", just "less ambiguous". In fact, just since 1987 a "less ambiguous" natural language has been developed: Lojban (http://en.wikipedia.org/wiki/Lojban).
Lojban still has semantic ambiguities, but it is free of the syntactic variety (think "Time flies", which could either be a command or a statement) and thus is a less ambiguous language than most others.
I still haven't gotten around to learning it though. Someday.
For instance, legal language HAS to be imprecise, otherwise no lawyer would ever agree to anything ever. So much negotiation every day goes into the subtle imprecision of clauses in contracts.
That's why there are courts -- to navigate the imprecision of both law and contracts and to give intelligence to ambiguity that could never be replaced by first order logic.
That seems very unlikely. In fact I'd guess natural language has to be imprecise to work.