There are four categories of people who give tzedakah ... [the fourth of which is] one who does not give and discourages others from giving; he is wicked (Ethics of the Fathers 5:16).
Since this passage is listing varieties of those who give tzedakah, why does it include a category of someone who does not give? Not giving is not a sub-type of giving.
In the effort to streamline everything and make life less complicated, we have centralized many things, including tzedakah. Communities often have one organization that has one major fund drive a year. Those people who wish to operate in this manner are certainly at liberty to do so, but when they insist that this unified drive be the only one in the community, and they discourage all other tzedakah collections or campaigns, they are actually infringing on the privilege of others to dispense their tzedakah as they see fit.
I have the right to invest in mutual funds and allow others to diversify my investments for me, but I also have the right to choose for myself which stocks I wish to own. No one has the authority to deprive me of the right to make my own selections.
The passage cited is indeed considering only those who give, but among them there is a sub-type of those who give only once to a centralized drive and refuse to give to any other collection. While they certainly have the right to do so, when they try to exert their authority to prevent other collections in the community, while insisting that everyone must give only as they do, their behavior is unacceptable.
If you give tzedakah once, you have done one mitzvah. If you give tzedakah twenty times (even if you give a smaller amount each time), you have done twenty mitzvos.