It's usually Merrycan high schoolers floating around the world that feel threatened by the presence in China or Thailand of non-native English speakers.
Their own motivation for improving their own language competence is often nil as they believe being born an English speaker is a quality certificate in itself.

Just how mistaken they are in this regard is borne out by the proliferation and popularity of Bushisms (some writers make tidy sums of money reprinting them and commenting on them; interestingly there are no "Sakrozyisms" or "Foxisms" although both Monsieur Sarkozy and Senor Fox speak English quite often, but without those give-away deformities.

Really, the main reason why non-native English speakers benefit other non-native speakers is plain: They have to deliver quality and constantly rise to the challenges a naturally hostile environment reserves for them.

They also think about those differences between languages and reflect on why their first tongue prefers structures alien to their second tongue.

That is why even a Chinese English teacher might be better suited to his or her students' needs - if said Chinese English teacher is enthusiastic, interested in the English language and open-minded.