And no, giving charity does no deny another a right. They can choose to forego their rights. And I would suggest not giving to those who do so out of choice.
Charity is a choice, not an obligation enforced through violence. As such it is the correct answer.
Whether we live in such a society or not, charity exists and provides for those who cannot or cannot yet provide for themselves. It works pretty well.
Is it in my interest to give to another? If I am free to make that choice then yes.