Yeah. Usually it means the former. The term evolved out of the 1940s, when studio chiefs like Jack Warner (who went so far as to slap "Jack Warner, Executive Producer" on the WB logo itself) wanted to put their names on as "producers" even though they had little direct input into a movie. "Executive Producer" most commonly means "This movie wouldn't have happened if I hadn't said 'okay'," and as such is usually little more than an empty gesture of respect extended to someone who really hasn't got any say in the creative decisions.
Rowling had them over a barrel, though, which is why she was able to dictate terms. No one who is not a director has been able to exercise that kind of clout over a project since, probably, Margaret Mitchell.