I received the email from https://healthvana.com/

Los Angeles County gave me the vaccine, but Healthvana sent me the email to download the digital certificate so I assume that there's some kind of collaboration between the two to manage the record keeping for the who was vaccinated in Los Angeles County.

The CDC? All I got was that white card from them, as a matter of fact they probably don't even know I got vaccinated. They're so far removed from the distribution of the vaccine.

I would carefully check the emails from when you signed up or got the results and see if you can find that a business is actually keeping your records and not any government agency. I'm going to bet most government agencies will outsource the collection of data to manage appointments for vaccinations as most governments really struggle with managing large amounts of data (i.e. unemployment claims) or don't have the budgets for such systems.