*I am not a lawyer* but it seems to me that the airline should be responsible.

When the airline advises passengers to "use caution when opening overhead compartments as items may have shifted" they acknowledge that there is a risk posed to passengers by falling luggage. By advising passengers they are taking a small step to mitigate this risk, and they are choosing not to take further steps to mitigate the risk.

Of course this begs the question what additional steps could be taken to mitigate the risk. Would improved design of the overhead compartments reduce the risk? Perhaps different procedures, or restricting the weight/types of luggage that can be stowed in the overhead compartments.

An extreme (but possibly impractical) position would be to disallow the use of overhead compartments altogether. It is within the airline's purview to take this position, despite the fact that it may not be well received. However the fact is that the airline could take this extreme position and eliminate the risk posed by falling luggage. Therefore I say that the airline is culpable for any harm to passengers from falling luggage.