Commons relates to access, not ownership. Ownership relates to property and the sine qua non of property is ability to exclude. Everybody owning something is a non-sense statement in the context of public policy. As both a legal and practical matter public property is owned by specific governmental institutions so that access can be efficiently controlled.
Tragedy of the Commons describes the exact situation where people have unfettered access to exploit a resource, capable of deriving a personal benefit to the detriment of everybody else; and specifically such that exploitation of the resource produces significantly less social benefit than if access were limited. It doesn't matter if 99% of people are conscientious and abstain from unfairly exploiting the resource because of a cultural sense of transitive "ownership" as a citizen or human. The laws aren't for the 99%, they're for the subgroup of people willing to subvert the norm for personal gain (and to be fair everybody has been and regularly is a member of that subgroup at some point).