I don't think this is technically correct - as Bernstein-Von Mises guarantee under certain conditions that the posterior is independent of the prior after sufficient data is observed.
http://en.m.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_t...
http://en.m.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_t...
You're correct about the general case, of course.