The warning about the Local Backup means that if you were to lose internet during your tournament, the system won't be saving a most up to date backup of the bracket.
In the past, most tournaments would upload the Printer Queue tool which would print match cards, but what most people didn't know was that it was also saving a most up to date bracket on your computer.
Now adays a lot of tournaments are going away from printing match cards and using the player app to advance the bracket. So they are no longer downloading the Printer Queue tool. Which means you are not getting an up to date bracket backup.
It's not the end of the world, because a lot of times, phones can get access to the bracket via their personal data. BUT if you want to have a bracket back up in case of internet outage. You want to download the Print and Scan tool. Log in and Choose your event.