How to politely encourage academic integrity in non-academics? To give context for the question I have volunteered to do some work for a local charity. The work they do is literally lifesaving and almost certainly something the government should be responsible for, but the reality is that various charities are filling the breech. 

What I will do for them is data processing, they have messy data and they want some estimates for things they didn't record at the time. They will use the results to apply for funding for further work. 

In one of our meeting the topic of negative findings came up, for instance, what if their work isn't cost efficient compared to charity Y? The immediate response was a sort of joking "Oh we will bury it!". 

I was too uncomfortable to say something at the time, but I absolutely do not want to bury any findings. I understand that other charities may be burying bad findings, and refusing to do so may put this charity at a competitive disadvantage. Having read about what this has lead to in the pharmaceutical industry I know that this is probably more serious than anyone in the charity realises. In the long term it could completely undermine the causes they work for. 

Unlike scientists in the pharmaceutical industry this work is not my primary research topic, and I'm not being paid for it. My continued employment at my university is not threatened anything this charity do. So I could just read the them riot act, however I suspect if I do that they will say "Oh sure" and then ignore it later. I need to be diplomatic and convincing. They care about the work they do, but they also care about their own organisation, and asking them to do this is good for the work but bad for the organisation.

How can I best approach this?
Ask for another meeting. Explain politely that you were very concerned by the "bury it" remark.  See what they say.  With a little luck, it'll end there.

If you're not satisfied, you can ask for a letter explaining how they will handle any negative results and make your continued volunteer work contingent on getting a letter that's satisfactory to you.

If you don't get it, walk.  The inefficiencies you're worried about will eventually come to light, and you don't want to be tarred with that brush.

Edit: The remark from Pam to the question has very good advice for conducting the meeting I suggested.  A positive approach early-on is quite likely to lead to a satisfactory conclusion, without need for letters, etc.