Has anyone here recently got verified with basic verification?
As fare as I know nobody got verified with basic verification. Everyone has to go threw the enhanced verification process.
Doesn't matter if you live in US or another country. You are forced to do enhanced verification even for 0.1BTC
I would like to know that too. After basic verification I will just get: "We could not match your information to our public record providers."

I got this in an (automated) e-mail today:
"We are actively training new personnel and streamlining our processes to better handle the increased demand. Specifically, in the next week, Bittrex will be more than doubling our current support staff to handle the growth. The hiring of support agents will continue until we can provide the support our customers expect. "
Let's hope it's true!