Who Runs the Association -- Management or the Board of Directors?

That's an easy answer -- the Board of Directors!!

Strange how many boards or management companies do not understand this simple concept.

The management companies are agents of the association.  They are not the board of directors and they must follow the wishes of the board of directors, who make decisions by a majority vote.  The board of directors relies on the management companies for advice, but if you ask me that's often like asking a refrigerator repairman to fix your automobile.  Taking legal advice from a non-lawyer is definitely not a good idea and seeking the advice of an attorney is the best way for the board to protect themselves from personal liability.

Boards often give management companies the authority to make some decisions on their own, like obtaining services for repairs under $500, or sending out violation letters to homeowners after an inspection.  Management companies should not be making board decisions, such as hiring or firing vendors without board approval, sending out intent to lien notices unless a pre-approved policy is in place, or worse yet, sending an owner to the attorney for collections or violations without the approval of the board.

Some boards give the management companies full discretion to operate and manage the association as they see fit, but I know of at least one instance where that did not work out so well for the association in court. 

If the board members don't want to do their jobs, then turn the job over to someone else!  If the management company doesn't want to follow the board's direction, get a new management company. There are a lot of good ones out there, you just have to find them.