The evaluators care whether the courses cover the same things in the same way. They don't care what things the nursing department wants in a stats class. Nursing is big on "evidence based practices" which requires you to be able to evaluate the results of research - to understand what the numbers/graphs are saying and to tell whether a study is well designed. So a basic plain old stats should is probably all they require.
I looked up business stats and plain old stats here .... they cover the same things but in a different way. The business stats is calc based and the plain old stats is not. So, if your school has the same kind of business stats - you should not have to take stats again. And it probably does, which is why you can't take the stats if you have credit in any other stats class... it would be like getting credit in "basic math operations" when you already have credit in "college algebra". They don't really care that you wouldn't learn anything (my humble opinion based on how often people don't learn much in a class) but they probably need the credits spread across different catagories of classes for accredidation purposes. That doesn't really apply to you but it would in general, as stats is required in a lot of majors.
The easiest way might be to talk to the people at the math department and get confirmation that your class covered all the required stats class does - it doesn't matter if it covered more than that. It would help to print out copies of the course descriptions and objectives of both classes to take with you. The math department people are more likely to undestand the differences in the classes than the nursing advisors. The nursing advisors will probably take the advice of the math department about this.
Then talk to a nursing advisor that has the authority to waive requirements - or to sign off that you covered that class... whichever they want to do. You will probably have to start with a general advisor or general advisor who specializes in the nursing program - keep going up the ladder until you get to someone with the proper authority. You may need to leave your request with them to discuss with other nursing advisors. I'm cynical but with much reason.
) In my experience, advisors usually mean well but are only dependable about f.a.q.s, and distinctly not dependable about unusual situations.