The problem is that the Divx codec is licenced.
If this is the first console you ever downloaded it onto it should work offline. If you have downloaded the update to another 360 in the past with your gamertag it will only work whilst you are logged into live with that profile.
It's all to do with how M$ does their content licencing. The content is licenced both to an online gametag and the console it was first downloaded on. So in short, the content will work offline on the very first console it is ever downloaded onto or on any console with the gamertag it is owned by as long as the GT is online.
Given you wish to avoid the fall update, your only options to get divx content working again will be to use a program on your PC such as Tversity or Ord or any others people now recommend (Media Streaming Software, you'll have to do your own searches on these). It will also give you access to other formats like .mkv etc by using these, so there is a little bit of a plus.
Generally what people should do, when they want to avoid updates or being bricked with bans and still use all their content and arcade games etc is to transfer the licencing of all their content to the current console they use. (This is done through xbox.com with instructions). The only hassle with this method is that it can only be done once a year for your Gamertag.