They are more subtle. They say there is no “automatic advantage”. That doesn’t rule out that ED all things being equal offers an advantage.
All elite schools say that they won’t accept people ED that they wouldn’t accept RD. The degree of advantage for ED (if any) is never disclosed.
Given the acceptance percentages and the fact that elites tend to draw about half their incoming classes ED suggest an advantage exists even once offset by hooked ED candidates.
This is actually Brown’s statement on ED advantage.
“Our pool of early applicants tends to include a very high proportion of exceptionally talented students and a higher rate of admission for Early Decision applicants reflects that phenomenon. However, it does not imply an automatic advantage for all early candidates. We admit Early Decision applicants only when we are confident that we would offer them admission as a Regular Decision applicant.”
Most qualified college counselors will advise applying ED if you have an affordable first choice. Particularly when looking for single digit RD admissions schools.