Part of the problem is that the relevant RFC 2183 doesn’t really state what to do with a disposition type of “inline” and a filename.
Also, as far as I can tell, the only UA that actually uses the filename for type=inline is Firefox (see test case).
Finally, it’s not obvious that the plugin API actually makes that information available (maybe someboy familiar with the API can elaborate).
That being said, I have sent a pointer to this question to an Adobe person; maybe the right people will have a look.
Related: see attempt to clarify Content-Disposition in HTTP in draft-reschke-rfc2183-in-http — this is early work in progress, feedback appreciated.
Update: I have added a test case, which seems to indicate that the Acrobat reader plugin doesn’t use the response headers (in Firefox), although the plugin API provides access to them.