Without knowing more about your F5's configuration I would suspect you're correct, something is misconfigured within the HTTP compression profile for the virtual server.
BIG-IP will take the accept-encoding header from the client, and inserts a content-encoding header for gzip or deflate determined by the original client request. If the virtual server is not setup for HTTP traffic or does not have an HTTP compression profile I could see you having issues with proxying the accept-encoding and returning the content-encoding header.
My BIG-IP v13 HTTP compression profile defaults to gzip for preferred compression method.

If your virtual sever has an HTTP profile and not an HTTP compression profile, start by copying the default to a new profile and toggling this. If you're BIG-IP is older than v11, this field is in the HTTP profile. Give this a whirl and see what happens.
Check out F5 KB15434 for more information on this and if all else fails, DevCentral Q&A may have some more details on this.