If 2 airlines have interline baggage agreements, luggage can be checked through to along the route, even if on separate tickets. This goes beyond Alliances. As Davvidd and I mentioned, it sometimes requires a more seasoned agent at check in. There may be some countries where it is not possible like when the International and Domestic terminals are physically separated but even those might be a questions of picking up in one and dropping on a conveyor in the other.

The other thing is that there is a maximum flights on one tag (I believe it is 4) so sometimes a second one pops out. That also confuses some less experienced agents.