Don't forget the biggest variable which is the actual manhours spent in an encounter. You learn by doing.
Those people who you see on videos have easily spent 10 hours on a current endgame encounter.

The fact that t13 was killed 5 days after the patch with ilevel110 gear stands as testament to the fact that gear doesn't play as big of a part as most people think it does.

With regards to internet connection, people cry lag all the time, even on streams and videos when you can obviously see in it that they are being hit and their reactions are simply too slow.
Personally I play with a ping of 150-200ms and encounter none of these issues. You don't need "top class internet" and 99% of the time you can only blame yourself for being hit.