Do you have a test site you can test this out on, or is your production site the only one you have access to?
As far as I can tell, old versions of Multisite don’t have that site option in their databases. Newer installs (Dec. 2012 and later) seem to have that option automatically set to 0 so that they will avoid using ms-files.
It’s strange. It seems that the option not existing in the database at all causes WP to use the old ms-files style; the option being set to false in the database causes WP not to use the old ms-files style; I haven’t yet found an example where that option was set to true/1, so I don’t know what effect that would have (presumably the same as the option not existing).
If you have a test version of the site, it would be nice to see what changes if you delete that site option from the database, and what happens if you manually set that option to 1. I *do not* want you doing this on a production site, though (I know you well enough to know that you’re thinking of doing that), as it could potentially really screw up all of your upload locations.