Question: if someone creates their own database, are they allowed toIf by "their own" you mean that the entire database table is created by a single someone, then yes of course: that person is always free to give himself/herself permission to publish his/her own content in other venues.
In other words, Yahoo in its TOS does not claim ownership of the members' contributions, it only claims non-exclusive license to display the contributions.
For databases built by multiple contributors the situation is murkier. As far as I know Yahoo's TOS doesn't distinguish between different types of content: the member's contribution is the member's contribution. In Yahoo Groups it would be possible, in principle, to distinguish the rows contributed by (or last edited by) each member.
That said, I don't think the current implementation reveals authorship for database content in any way (not in the database itself nor in the activity logs). I don't remember specifically, but I don't think Classic did either. So there are practical difficulties with respecting ownership of members' content within the database. The question of "allowed" then boils down to a question of how a dispute could possibly be decided. With a total absence of evidence of ownership I think the members would have to simply look upon the database table as a collaborative content, with no part of it specifically owned by any member.
But I am not a lawyer, so if you move a database and end up in a dispute with other people about their ownership of the content don't cite me as giving you permission.