Help with good RDBMS transactional schema design that mimicks a sports league
I imagine that most sports leagues don't change their hierarchy of conference, division, etc... very often so it's probably safe to have each level in its own table.

If your goal is a system that can handle different leagues that have different hierarchy depths, then the recursive table approach is probably better. 

I don't know how easy it would be to do this with an ORM but I have a general mistrust of ORMs when it comes to anything other than simple CRUD operations... To prevent a team from existing at multiple tiers of the hierarchy, I'm not sure why your proposed Team.LeagueGroupId wouldn't work. You know what level the LeagueGroup referred to by LeagueGroupID is so you know that the team exists at the level of that LeagueGroup.