Why does my browser think that it's Chrome? While browsing the web from my phone, I currently use the stock browser. However, I've encountered a curious problem.

If I go to a page, and then switch to another tab, it will often take the tab that I was on and turn it into this:

 

It puts data:text/html,chromewebdata into the URL, so it shows a page with chromewebdata. 

In addition, for a while, every time I Googled something, it would show me 'We've detected that you're using an older version of Chrome' blah blah blah. It also switched itself to the desktop view. (When going to get a screenshot for this question, however, that magically fixed itself, so...)

Why was this happening?
As Andy commented, some Android stock browsers are based on chromium.

The issue you explained is kind of a bug where Android WebView built on chromium fails to loads the page in question due unmapped ssl error.

As explained here: https://bugs.chromium.org/p/chromium/issues/detail?id=395638;


  Android Kit kat WebView component built on chromium is unable to open
  web page due to an unmapped ssl error! It is usually  occurring on
  secure login pages presented by captive portals.


Here is their extracted log entries

04-09 12:49:49.215: W/chromium(24516): [WARNING:ssl_client_socket_openssl.cc(182)] Unmapped error reason: 261
04-09 12:49:49.215: E/chromium(24516): [ERROR:ssl_client_socket_openssl.cc(870)] handshake failed; returned -1, SSL error code 1, net_error -2
04-09 12:49:49.245: E/WiFiWebLogin(24516): ExtWebViewClient - ExtWebBrowser-veiw-1 - onReceivedError: errorCode=-1, failingUrl=https://1.1.1.1/login.html?redirect=syslynxservices.com/ description=net::ERR_FAILED
04-09 12:49:49.265: I/chromium(24516): [INFO:CONSOLE(12)] "Not allowed to load local resource: file:///android_asset/webkit/android-weberror.png", source: data:text/html,chromewebdata (12)


Had the same issue, and what stuck me is that they sugested it usually occurs on secure login pages by captive portals which is right where I saw that funny message telling me "we have detected a you are using an older version of chrome". 

Could'nt come up with a solution but had to switch browsers but like you noted the issue vanished away eventually.