The question is: should the server have performed the update to /People/Bob?
From the HTTP spec, a 406 means:
The resource identified by the request is only capable of generating response entities which have content characteristics not acceptable according to the accept headers sent in the request.
Unless it was a HEAD request, the response SHOULD include an entity containing a list of available entity characteristics and location(s) from which the user or user agent can choose the one most appropriate. The entity format is specified by the media type given in the Content-Type header field. Depending upon the format and the capabilities of the user agent, selection of the most appropriate choice MAY be performed automatically. However, this specification does not define any standard for such automatic selection.
Note: HTTP/1.1 servers are allowed to return responses which are
not acceptable according to the accept headers sent in the
request. In some cases, this may even be preferable to sending a
406 response. User agents are encouraged to inspect the headers of
an incoming response to determine if it is acceptable.
If the response could be unacceptable, a user agent SHOULD temporarily stop receipt of more data and query the user for a decision on further actions.
That note in the middle about HTTP/1.1 may be your answer. I read it as saying "you may return a 200 in response to the PUT request to /People/Bob when the user agent specifies application/xml in the Accept header, selecting any suitable content-type, and that this outcome may be preferable to returning 406."
Under this scenario, the PUT would succeed on the server, return a 200, but the client would get an application/json representation. The client needs to be able to handle that possibility by making sure that it understands the media type given in the Content-type header, and behaving in a well-defined manner if it doesn't.
But this is always true anyway.
One more thing: you may want to consider not using plain-vanilla media types like application/xml and application/json, but instead define your own custom media types, maybe based on XHTML or JSON. All of the client-server coupling in a RESTful application happens through media types. Without media types rich enough to capture your domain concepts, you're incompletely specifying your REST API.