Actually, I think "identifierForVendor" does it mostly.
What's odd about the article is that access to the UDID was removed at least by iOS 7 in 2013 and maybe before. So by 2015 when this supposedly happened, was this only affecting non-upgraded devices?
At the front of the thread, it states the info comes from an NYT article published just yesterday:
https://www.nytimes.com/2017/04/23/...s-uber-and-himself-to-the-precipice.html?_r=0
Click the link and read it for more details. This is good practice for any forum's news posts, btw. Always check out the source material. Often important info can be distilled out.