Supporting policies that insure that the poor and elderly have income and health care they can depend on, that they don't have to beg for or go to a church and let evangelizers wash their feet for, is charitable as well.
I live in a red state, and the poor people start making the rounds at the churches as the month wears thin. The immigrants, of course, are hardest hit, because any agency that gets government funding (e.g. the food pantry) can't help them because they're undocumented. Churches will give to anyone, but their only reliable source if they don't have an off-the-books job is the Salvation Army, which gives out food once a month.
I know that poor people are very generous, and very generous to one another. I've never experienced poverty, because even when my husband was unemployed the severance pay covered it (except for about one and a half months, I think). But I've had friends in all sorts of economic circumstances, have lived in a lot of places, and have gone on mission trips, so I've seen poverty first hand. I've helped friends through difficult circumstances, too, which is the kind of charity that isn't reported. I'm sure you all have, too.
Once I sent a Wal-Mart gift card anonymously to a friend at Christmas, taking pains to hide my identity (driving to a different post office, typing the envelope, etc.) She and her children visited us at Christmas for dessert. I didn't have any gifts for her because I didn't want her to feel embarrassed that she couldn't reciprocate, but when she arrived she had taken part of the Wal-Mart GC and gotten gifts for the five of us. Yes, the poor are generous.