I've never heard a sentence in actual usage[1] where the usage of the singular "they" was ambiguous.

In terms of being understandable and elegant, the singular "they" is probably the best English can do. Unfortunately, it's not widely accepted because it "sounds" uneducated, despite being the current best solution to the problem. Gender-neutral neologisms, like Spivak pronouns [http://en.wikipedia.org/wiki/Spivak_pronoun], are not commonly understood, while constructs like "he/she" or randomly alternating between generic "he" and generic "she" as in the OP is inelegant and confusing (hence this whole thread).

[1] I'm sure you could construct a contrived example.

Fragment. Damned good device.

Written language has more legitimate uses than completely formed sentences. Pronouns can be troublesome enough, figuring out the antecedent, without requiring yet more context analysis.