The DGA Membership Directory is available on-line. Quentin Tarantino, Robert Rodriguez, and Alexandre Rockwell are not listed. Allison Anders is listed.
Here ’s an article that explains in much more detail about the specific issues that come up (for both the studio and the individual) when a director’s not a member. An excerpt:
The guild has stuck to a one-director-per-film policy since 1978, to keep producers and stars from demanding “gift credits.” Exceptions are made under special circumstances: The guild recognizes “bona fide directing teams,” like the Coen brothers, the Farrelly brothers, and the Wachowski brothers; and the policy can be waived for directors on films with multiple languages or stories. Rodriguez was unable to get a waiver for Frank Miller, who had never directed a movie before, so he quit the guild…
Using DGA members can cost a lot of money because the basic agreement specifies minimum salaries for each guild member on the crew. A director, for example, is guaranteed between $8,000 and $15,000 per week, depending on the size of the production. The guild also ensures that its members receive fees (called “residuals”) when the film is released on video, DVD, and television. On the other hand, many of the best assistant directors are guild members, and skilled personnel can often save money for a studio by making sure the work gets done on schedule.