claiming the tax back
That's interesting. I don't know about the US, but here down under, donations to registered charities are tax deductable, but the taxpayer claims the deduction from the ATO (local Revenue equivalent). The charity doesn't get the break, only the benefit of the incentive.
UK 'gift aid' arrangements seem better, except that they're still a distortion of the tax system. I'd rather see these deductions abolished, along with a lot of other loopholes, like family trusts.