Safari on iOS did not tell me "you don't have internet connectivity", but it did say that servers were unreachable (not surprising) and it let me use local servers without issue. iOS seems to prefer WiFi to cellular when it's available as it didn't fall back during my limited test.
This is the behaviour that I'd expect from the Smart TV. Just because it can't get to Samsung doesn't mean it can't get to Netflix.
I imagine if Apple's DNS settings got screwed up or their server was throwing up something other than "Success" due to an error, iOS devices around the world would claim their Wifi needed a login and wasn't working.
edit: another comment further down linked this article that says that exactly the same thing happened to iOS http://www.zdnet.com/what-went-wrong-with-ios-6-wi-fi-700000...
The results might have been different if I had ran the test longer or turned WiFi off and back on or something.
www.isg-apple.com.akadns.net 571 requests in the last day
us-courier.push-apple.com.akadns.net 558 requests in the last day
.akamai.net 709 requests in the last day
and
.akamaiedge.net 1967 requests in the last day
--
I believe Google just uses *.l.google.com (my open dns says 1202 requests in the last day)
Imagine if your Samsung phone couldn't do anything that required an internet connection because Samsung's site was down. This is pretty much the same thing, IMHO.
Samsung's site being down or unreachable should have no bearing on the performance of the Netflix app whatsoever.