Sorry, but "NEVER hire someone because you want them to do what they have done before - that kills your show" is indeed nonsense as a broad, flat-out statement.
No, you wouldn't want an actor to TOTALLY pattern their performance of a new character in a new show after a previous performance in another show, but I don't think any decent actor would ever do that. On the other hand, audiences love certain actors for certain talents, abilities, and mannerisms, and they love seeing those things displayed in various shows.
Of course, it's also GREAT to see an actor stretch and play a completely different kind of role than they have played before -- if the stretch is successful. Many actors do this all the time, and are often admiringly labeled "character actors" rather than stars with very strong, definable onstage personas.