That is far from clear to me based on what they've published, but I believe it means the latter, but I am only about 80% confident in that answer.

I think the best evidence to support that is on this page where they state "Delta Reserve Credit Card Members will still have a higher prioritization within their Medallion peer set for upgrades." which is the same language used for the Corporate Accounts, so it appears that priority is similar to what Reserve members have received, which my understanding (and belief based on personal experience) is that it is just a tie-breaker if you have the same fare class, it doesn't put you above higher fare classes.