Should a small business that is cash rich, pay the $5000 deductible for one its employees having carpal tunnel?

Absolutely! $5,000 is a very low price to pay, given that the company would likely have to pay a lot more if the employee decided to sue for such a job-related injury. $5,000 may very well be the difference in being sued and not being sued. Not paying could indeed be the straw that breaks the camel's back.