That's a clever example, but why would you do that? The avatar should be a static resource. As such, I'd only provide an upload file dialog.
Quit being overly pedantic about how contrived the example is and struggle with the underlying fact that the compression type is negotiated between the client and server. If the compression happens on the HTTP request (as some of the comments here suggest), then the server must use that compression method or it fails to read the body of the request.
That's basically one of the core ingredients of security. Build a threat model.