A person with J2 visa is allowed to study part-time or full time.
http://travel.state.gov/visa/temp/types/types_1267.html (version December 2007)
See "Spouse and Children":
Study- The spouse and/or children of an exchange visitor visa holder who are in the U.S. on an exchange visitor visa may study in the U.S. without also being required to apply for a student (F-1) visa or change to F-1 status.
Also:
http://www.hooyou.com/nonimmigration/type.html
Please reconfirm your source for this particular issue. Information about eligibility for J2 study is also seen among all University international affair offices.
I do have a friend studying in our state with J2 visa, while holding an EAD to work part-time.