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Sounds very fishy. If this really is a charity, the band's management can agree to limited use for charitable purpose and take a substantial tax deduction going forward. In fact under some conditions the tax deduction can and will be more than the fee they want to charge for use of the work product. Moreover, the charitable organization would have to provide public attribution so there would be additional publicity for the original work product.
If the band's management owns the work product as IP they may own it outright the same as you owning a car (assuming its paid off) or a bucket of fried chicken (assuming its paid off).
Someone attempting to induce you to utilize the work product for a purpose not authorized by the owners is possibly criminal in intent.
So, will this charitable organization "save, defend and hold you harmless" if you, at the behest of the charitable organization, utilize the work product? Will they go to court and defend you and pay all legal fees and fines without limitation, and will they somehow (through liquidated damages) repair any potential damage to your reputation? Whatever the answer to that question is, is the answer to YOUR question.
Of course you can't legally cover someone else's track, and by doing so I'm assuming you would be opening yourself up for a lawsuit- that of which the production company certainly would not protect you from (they probably would be the main ones sued anyway).
Now I have heard of cheaper licenses that bands/artists will give out that allow other bands/artists to legally cover a song for a specific situation, but even in those cases the said covered material that you produce needs to sound like a different version and not like you are trying to literally copy the original track. If the production company purchased this license or not would be the determining factor for me, and even if they did I still would probably pass. Ask who their intended audience is and try writing something original, out of the box, and specific to that audience to see if they like that instead (probably won't work but you never know).