I think I see the fundamental point where we disagree. I try to keep as much business logic in the database as possible. That's more of a DBA perspective, I guess: don't trust these pesky app developers, always assume they'll try to put broken data in your DB.
It's often not possible to model all business rules in SQL, but the more you manage to cram into the database, the less probable it is you'll end up with inconsistent data.
Often there are dozens of applications (or independent modules) using the database. Keeping the business rules (like "every user has to have a first name" or "no two customers can rent the same car at the same time") in a centralised place helps a lot with keeping everything in order. It's often not possible to limit the interaction with the database to a one-and-only system (imagine different teams writing different parts of the system, app changes, outsourced integrations, etc)
So, if a label can't have spaces in it, that's easy - slap on a check constraint that enforces it. Then you know that even if the new hire writes a "change my label" funcionality and forgets to enforce the no spaces rule, she won't screw up your data.
If a user can have at most three labels, things get more interesting. Offhand I'm not sure how I'd model that and it actually is a difficult problem, best solved with triggers IMHO, as you have better control over locking and can guard yourself against concurrency issues.
Anyway, the discussion on "all logic in DB" vs "all logic in the app" is part of the neverending struggle between DBAs and app programmers...