Dear Jasen,
As a former violinist who moved over to the viola (my hands just really got too big for the violin in the end), it depends. They are separate instruments, however some people happily play both (say, Nigel Kennedy). The following are the main considerations for a viola player:
1) Intonation might be a bit of a problem - the notes are a little closer together
2) If they are a bloke (usually) with big hands they might have trouble with their fingers falling all over theirselves
3) The lack of a C string, and the sudden addition of an E string might put them off
4) They may well be more used to dealing with the alto clef than the treble clef
However, the difference is mostly in the type of parts they play. Violinists are used to being "front and center", tend to have the leading part and, frankly, in their career, having to compete with a lot of violinists (and there are a lot more than violists). Violists often have accompanying parts, fewer solos etc. I would say it is easier for a "native" violinist to move to the viola, than for a native violist to move the other way, on the basis that the parts are usually (sweeping generalisation here) less demanding and exposed. But the mileage of each violist will vary.
Bottom line - if the violist says that they can do it, assume they are correct until you hear them. A violist who does not feel comfortable will tell you without even trying it.
Hope this helps.
Kind Regards,
Nick.