THEY DON'T WANT STUDENTS WHO ARE NOT COOKIE CUTTER

I know what you mean. Why would you go for a Masters in "Business" Administration if there are Masters in Science of Administration more suitable to non profit applicants. I'm working in the NGO sector for 7 years already, and my 2 cents are: if you want to be a project director, or project manager, or write proposals, or work in the administration of an NGO (actually this is too ample and should mention which kind of organization we are talking about), for example a non profit that specializes in relief projects and development, then the MScA is ok.

For folks like me, who worked in the finance department of the organization, and need a masters to improve not only the skills related to management and administration, but also related to accounting, procedures, finance operations, and want to work in a higher position, maybe in the head quarters of the organization, then the path to follow would be a corporate finance concentration (a Masters in Accountancy may do if you want to specialize in the financial statements preparation).

I studied accounting in the university and worked as an accountant in the Development and Relief NGOs, then as a finance officer, controlling the expenses according to the sponsors regulations, and reporting periodically. I also worked in a church organization (which is an NGO but the business structure is totally different).

I envision 2 possible post mba paths:
1. return to the Relief type of NGOs, where I want to specialize in preparing a standard set of procedures for relief projects. My ideal position would be working in the Head Quarters of the organization, and as soon as a disaster appears, deploy a finance team to implement the procedures right away (often the local office is not ready to efficiently use the large amounts of money and properly report afterward). Would also be involved in typical compliance process visiting local offices in several countries making sure they follow the global organization's financial reporting standards.
2. work for my church organization in any of their continent regional offices or even the head quarters, in the finance department. Work in a team that develops standard procedures for the different countries in the region, and later would like to work in the team that makes the decisions about investment of funds (retirement fund, atypical tithe, etc). In this organization, it was normal that pastors would run the organization, even the finances. As the world developed, more finance people are now in positions related to finance, but not administration. Some offices still depend on pastors to make financial decisions, and though the trend is moving more towards a professionalized job description (a person that studied to be a pastor will work as a pastor, and the one that studied accounting will do the accounting work), still there is room for improvement and the organization still looses money in their investments.

For any of my career paths that I could choose, a MScA will not make any sense. I would need a MBA strong in Finance, even when I'm not going to work in IB or as trader, I need to take some classes about capital markets, and most of the classes about corporate finance. Top programs include electives specific for NGOs, so that makes perfect sense for me.

I think that the key are the post mba goals: if you can show that you need the MBA rather than any other program, then there is no reason why they should not admit you. You can see the stats, every year bschools admit several non profit guys.