(There are some cases where identifiers are pulled in from other systems, but none of them can be used as the basis for unifying users.)
Analytics doesn't either, it uses regular cookies. (See sibling comments.)
I don't know why HN seems to be so stubborn about things like this. It's clear as day they fingerprint users, but seems like the majority of users here refuse to believe a corporation or government has done anything wrong unless they literally admit it in a press release.
GA isn't nearly as invasive as people think. The real problem is data being combined on the backed and correlated across websites by ad networks, not the analytics itself.
Edit: Worth a look if you're interested in what's being collected: https://developers.google.com/analytics/devguides/collection...
Unfortunately, that sounds exactly like the set of information that can be used to fingerprint users.