Can you explain the way this works? I hear stuff like this all the time, but my (admittedly limited) tax knowledge says this is not possible. Donations to charity allow you to reduce the gross income you are taxed on (in the US at least). However, you are not saving any money this way. The top tax bracket is basically 40%, so if you donate 1 million to charity, you reduce your gross income by 1 million, saving you at most 400K in taxes, but you donated 1 million, which means you lost an extra 600K vs just paying your taxes.
I don't know whether that story is true, but if so, it would be done by putting the money into a 'charitable' entity that returns the money in a less- or non-taxable way. This is not really something that could be done in the United States outside of fraudulent activity.