It Just Makes Sense

My Theory: Billy Joe and Bobbie Sue shot the deputy  

That would explain everything.  We already know what happened to the sheriff.  

Exactly!  Everybody already knows that Bob Marley shot the sheriff.  He admits to it in the 1973 song "I Shot The Sheriff."  Of course, one could also make the case for both Eric Clapton and Warren G shooting the same sheriff, but while that does cause one problem, it does nothing to answer the one open question left by Marley.  What happened to the deputy?  

Everyone seems to blame Marley for shooting the deputy, despite his consistent protestations of "I shot the sheriff, but I didn't shoot no deputy."  I tend to take him at his word, however, since he's doing this while admitting shooting the sheriff.  At this point, he doesn't have much to lose.  He also claims to have a very valid reason for shooting said sheriff, but no motive for deputy shooting is ever given.  I'm just supposed to believe that he went on a shooting rampage with no prior history?  I don't think that would fly in court.  

However, we know the story of Billy Joe and Bobbie Sue.  They are known criminals with a history of burglary and gun violence.  Canonically, there was a shooting during a home invasion in El Paso, where they ran into a great big hassle.  They were pursued by a detective named Billy Mack, but never apprehended, as it is claimed they are still running today.  

What is also mentioned is that they headed south from El Paso.  You know what's south of Texas?  That's right...Jamaica.  Now, since Bob Marley is Jamaican, I'm making an assumption that the shooting incident he mentions took place there...it seems like a perfectly valid assumption to make.  So, while Marley is perfectly willing to admit shooting the sheriff, I'm 83% convinced that Billy Joe and Bobbie Sue were the ones who shot the deputy.