As far as I understand the specs, the ETag, which was introduced in RFC 2616 (HTTP/1.1) is a predecessor of the Last-Modified-Header, which is proposet to give the software-architect more controll over the cache-revalidating process.

If both Cache-Validation-Headers (If-None-Match and If-Modified-Since) are present, according to RFC 2616, the client (i.e. the browser) should use the ETag when checking, if a resource has changed. According to section 14.26 of RFC 2616, the server MUST NOT respond with a 304 Not Modified, if the ETag presented in a If-None-Match-Header has changed, and the server has to ignore an additional If-Modified-Since-Header, if present. If the presented ETag matches, he MUST NOT perform the request, unless the Date in the Last-Modified-Header says so. (If the presented ETag matches, the server should respond with a 304 Not Modified in case of a GET- or HEAD-request...)

This section leaves room for some speculations:

• A strong ETag is supposed to change ''everytime'', the resource changes. So, having to responde with something else as 304 Not Modified to a request with an unchanged ETag and an If-Modified-Since-Header, which dose not match is a bit of a contradiction, because the strong ETag says, that the resource was not modified. (Though, this is not that fatal, because the server can send the same unchanged resource again.)
• ...

... o.k. While I was writing this, the question was boiling down to this answer:

The (small) contradiction stated above, was made because of Weak ETags. A resource marked with a Weak ETag may have changed, although the ETag has not. So, in case of a Weak ETag it would be wrong, to answer with 304 Not Modified, when the ETag has not changed, but the date presented in the If-Modified-Since does not match, right?