Shaine, 

It depends on your nationality and your employer/profession, the local's condition (i.e. was he drunk), witnesses, and the importance of the local amongst his fellow nationals.

Generally law enforcement favors locals, but not to the extent that the lowest local is given immunity against harming others.  I've been in accidents (both as the driver and as a passenger with locals).  In cases where it was clearly the Qatari driver's fault, he/she was cited.  In marginal cases, they received the benefit of the doubt.  In one instance the other driver (clearly at fault) attempted to blame my colleague and became very threatening.  When the police came they entirely dismissed him and told him off.  Having said that, I am a wealthy white expat with immediate access to Arab speakers and Qataris who work for either me or my company.  I wouldn't want to be a Sri Lankan maid in the same situation.

My advice is don't get into a physical fight with anyone, regardless of nationality.