Not sure that contradicts the claim. Publishing the CVE is what makes it public.
What did happen is that a whole bunch of people had no clue and called the fact that "these 2 CVE IDs will be used for a PHP vulnerability" a CVE leak. Posts were going around yelling "CVE leak!" with a CVE database link that said "no information yet". Part of this is the mushed usage of "CVE" to just mean "vulnerability" rather than "CVE record". But still, quite ridiculous, and annoying. Information that CVE ID XYZ will be used for project ABC is *not* a leak. Like you say, CVE publishing matters. Getting the CVE record contents would be a leak.