That [Ayn Rand] opposed private charity as well is a separate issue and one on which I part company with the lady.
OK, I have only read
Atlas Shrugged, but as a manifesto of beliefs it is pretty comprehensive.
From that, I would not say that Rand opposed private charity, but that she opposed charity for certain reasons. You should give to charity if you yourself take value from the act of giving; however, it is incumbent upon you to assess those who you are giving charity to. If you give them charity because the person to whom you are giving demands your charity as a right, and they are unwilling to stir themselves but are merely content to live off alms, then it is wrong to give to them. It is wrong to give to those in these circumstances, regardless of your personal motives, because your charity will trap them in a cycle of evil because they will then never have to bestir themselves to live by their own talents and hard work -- a situation that Rand believed to be absolutely immoral.
If, however, your charity will improve their lot or you give because that person has given you value (they are a friend, or have performed some past service), then you can give to them -- as long as you wish to do so. You should not do so because you feel guilty about it, but because your charity will help them to reclaim their lives and to make more of themselves through their own efforts.
That, at least, is my reading of her views; and, given the amount talked and written about, for instance, the Benefits Trap, it seems an entirely reasonable stance to take.
DK