They wouldn't need to access 14,000 separate accounts if they had internal access to the database.
The article states they got access to "private data" from 6.9 million other users via a 'DNA relatives' feature but doesn't explain what kind of information that is. For those accounts that got directly accessed, it seems unlikely the hackers requested and intercepted an email for every one without being noticed sooner. Sounds like they only scraped what's available on the site itself but it'd be nice if the article actually detailed that.