A majority of the directors of our 501(c)(3) public charity are currently the fund advisors for a donor advised fund. Most of our charitable contributions go directly to the fund at a community foundation. We then make grant requests to the foundation for our charitable giving to the community. How do we answer the question [on Line 44a of Form 990-EZ or on question 6 of Part IV of Form 990]: "Did the organization maintain any donor advised funds during the year?" I can’t tell if this would be “yes” for the community foundation but “no” for our public charity because we don't house the money, we just request certain donations be made from the fund.
Your supposition is correct. The community foundation would answer “yes” and you would answer “no.” The question is designed to determine which organizations actually sponsor and hold donor advised funds, not which organizations benefit from distributions from such funds. Those who sponsor DAFs may not file the Form 990-EZ. They must file the full Form 990 and answer a number of other questions intended to determine whether they are complying with the various DAF restrictions.
It is unusual for a public charity to direct its own charitable gifts to a donor advised fund at another organization. You only obtain the benefit of these gifts on specific recommendations to the sponsor of the DAF and those recommendations could be (although they almost never are) denied. The sponsor has absolute discretion over those funds. This practice certainly restricts your freedom in using the money and you may be cutting down on your own public support if you use the DAF to make gifts to others. It could be useful if you want your own organizational giving to other charities to be done anonymously. It could be useful if it “launders” major gifts from individual donors whose direct gifts to you would reduce your public support fraction so that you might flip into being a private foundation. You shouldn’t rely on this continuing, however, because the IRS is currently considering whether it should trace gifts back to the donor to the DAF.
I would want to know a lot more about your reasons for utilizing this approach before recommending that you continue it. But if this is your only connection with a DAF and you are not sponsoring DAFs and holding funds at your organization for others to make recommendations about, you should answer the question “no.”