Though I agree in principle, my experience making the pitch over the past decade has been there is no real connection between the mission values of nonprofits and the values of open source.
Nonprofits want a better vendor. They do not have the capacity or interest to break out of the "proprietary vendor" mindset. Therefore, the key to making the idea work is to use open source, ideas like social enterprise, etc. to create a "better vendor" in the eyes of the nonprofit community.
The nonprofit gets all the benefits that come with mission alignment, but doesn't have to understand or even be aware they are getting those benefits. The nonprofit gets a better product at a lower price point.
I'd take it a step further, and say there is often no real connection between the mission values of a nonprofit and the values of other, even related, nonprofits. Perhaps this is because resources are tight, especially with smaller nonprofits.
I would agree in principle, but I also have the experience that a lot of non-profit organisations initially just want a vendor who takes care of them. Althought they sometimes complain about vendor lock-in, they find it extremely hard to take their position as customer. In my field of non-profit (Dutch housing corporations) the more innovative organisations will take their first steps in open source in the next couple of years, but will still require support from consultants/support organisations. In that way they reap some of the open source benefits, but the consultant is the one who is really 'in' the open source world. We try to make that our playing field, and I believe non-profits will still profit on a cost level and on a flexility level. Also, for those that want it they can take the lead!