A friend of mine who lives in an Asian country noted that non-Asian Americans use chopsticks very well in American TV dramas.
Are talent doubles, and/or actor training, employed to ensure that this is the case?
No, they are not, as the use of chopsticks never plays an integral role in the making of a film.
In most films where chopsticks are used, the setting is a restaurant, an Asian or Asian-American home or an East Asian nation where chopsticks instead forks are used. It is simply easier to film the protagonists briefly using chopsticks to consume food than it would be to hire a chop sticks expert on their use.
Films are expensive productions. While some directors are sticklers for each scene in the film being "authentic", there are limits to authenticity. When characters are shown to be eating, the actual eating portion is the minor part beneath the dialogue of the scene and the facial expressions of the character(s). The majority of production simply could not afford to have eating process itself be "authentically portrayed" as the number of takes this could entail and the fact that scenes filmed may still edited from the final cut of the film would make this a waste of time and effort.
It's more likely that chopsticks "looks authentic" as it comprises a minor portion film thus any "mistakes" which may be made are ignored due to brevity of the scenes involved.