The basic verification definitely does not work. I entered al my personal info and it said it doesn't match public records.
Not sure why it doesn't work out for you, but I have a basic verified account, and have never had any issues. It's either you living in a remote area, or you living in a brand new area which the outdated verification system doesn't recognize.
In some cases people (not saying you are) even try to register themselves with nonexistent address information, which obviously will never be recognized by their verification system.
In case of the latter mentioned, Bittrex is cracking down on accounts who managed to use fake address information to get basic verified, which also contributes to those who are complaining about blocked accounts.