You are both right.  Nonprofits of all types, not just 501(c)(3) charities, that file a Form 990, 990-PF or 990-EZ tax information return are required to identify substantial donors (generally donors of $5000 or more) to the IRS on Schedule B, and must include the names and addresses of the donors.  But organizations other than private foundations and Section 527 political organizations may eliminate the names and addresses of donors when they make the Schedule available for public inspection. Therefore, you are undoubtedly correct that you have seen Schedule Bs without names of donors, and your colleagues are correct that the names must have been disclosed to the IRS.

The fact that 501(c)(4) advocacy groups and 501 (c)(6) trade associations are not obligated to publicly disclose the names of their donors has made them a very attractive vehicle for people who want to engage in political campaign advertising anonymously.  In the Citizens United case, the U.S. Supreme Court said corporations could engage in campaign advertising. Since (c)(4)s and (c)(6)s are permitted to support or oppose candidates in election campaigns—unlike 501(c)(3) charities that can lose their exemption for electioneering—many have opted to use anonymous donations for this new activity.