We've have our issues with Google showing the wrong date or false dates in the search results snippets. But how does Google determine the date to show or when to show a date in the first place?
John Mueller of Google wouldn't specifically say but he did say it is more than one signal to determine what date to show, or if to show a date at all in the search results snippet. I also suspect Google Search versus Google News has different signals they use as well.
Here is a screen shot of an article I wrote just a couple days ago. The same article shows one date in Google News (top stories) and another date in Google Search:
John Mueller said on Twitter "we use a variety of signals to determine which date to show, or if it makes sense to show one at all; it's not tied to one specific attribute."
So it isn't tied to specifically your date in your Sitemap file, your article byline, the first time Google discovers the page or something else, it is probably a combination of all of those things.
Forum discussion at Twitter.