It is true that you should be able to check your bags through if your itinerary is on one ticket, whether or not participating airlines are part of an alliance or not and regardless of the number of connections, though some agents might not be very enthusiastic about it claiming that their computers can handle no more than three segments.
Having one ticket is not a requirement. I have been able to check bags through to my destination even when travelling on two tickets on two or more airlines that are not a part of the same alliance.

General rule is that if you are on ticket, you can check your bags through.
If you are on two separate tickets and two different airlines, you can check your bags through if they have baggage handling/transfer agreement.
If the two airlines have ticketing agreement, chances are they will have baggage handling/transfer agreement also.

That said, the only place I have had trouble checking my bags through, when on two separate tickets was in MSY where the agent refused to cooperate even though NW had told me that they could. The agent was probably on a power trip as they also claimed that I should have checked in two hours ahead of time of departure for an international flight. I was on an international itinerary, but from MSY, I was travelling to DTW. Other than checking my passport and visa information, the agent had nothing more to do on account of an international itinerary. I checked in about an hour before departure.