Not a bad theory. Wouldn't need to be down to do that though.
There are not many reasons I could think to have chat be down during shootings. Seems like a big plot hole in the movie to me.
I can imagine it adding reliability and fast by making the service exclusionary for that period.
Another possibility is they put up a different version of the codebase during the event that integrates with other systems differently. Ie. connecting to another database or service outside or behaving differently for the purpose and then flipping back afterwards. This seems more plausible to me. Not sure how to confirm on the outside. It's just a guess unless someone leaks it.