I just updated one of my servers to 6.2. I'm in a closed environment (no Internet connection) and I have my web.conf set as:
[settings] .... updateCheckerBaseURL = 0 ----
Now the login webpage shows "Your browser could not connect to Splunk.com......"
This was good to go on 6.1.X.
Happened to me as well...
This isn't exactly my situation, but I came here from googling the error when I received it (new install of 6.3).
I discovered that I had an extension blocking content from quickdraw.splunk.com, which caused the page to throw the error. Backed off the extension settings and now it works.
(privacy badger on chrome, if curious)
Thanks a lot, you pointed me in the right direction. In my case the browser is firefox and the extension is badger just like in your case. Again, thanks a bunch.