I have asked the same question to some oil mfgr folks before, they all said the same thing. They have to make their oil compatible with other brands of oil, they say you can mix theirs with others and others with theirs, (including synthetic and mineral oil mixing) without degrading the previous (or new) oil. Every time the oil gets changed the new oil mixes with residual oil left in the engine..even if the same brand it has xx thousand miles already on it, (think about how many people do oil changes at various quick-lube places and can't even tell you what kind of oil was used last time..)
I have read articles that have said that even a 25% mix of synthetic will give almost as much benefit to oil quality as having 100% synthetic anyway.
Any oil that cannot be mixed with other brands should have that stated all over the bottle, and would also limit their appeal to any large customer base.
If a vehicle is burning a lot of oil, probably should carry plenty of oil with you anyway as you would be adding it frequently anyhow, otherwise adding top-off oil is probably coming up on change time soon anyway.