I doubt the committee thinks this way, but in my view you generally shouldn't be a number 1 seed unless you at least make the tournament finals in a strong conference, because it means at least two teams in your conference are playing better than you are (going into the NCAA tournament). Obviously a team as (mostly) dominant as South Carolina is an exception (or powerhouses like Connecticut and Tennessee in previous years): South Carolina could have lost their first SEC tournament game and wouldn't even have been pushed out of the #1 overall seed. And you need to have a strong enough resume up to that point (so forget Tennessee or Washington State).
The candidates still standing for 1 seeds in my opinion should be South Carolina (obvious), Iowa, Virginia Tech, Connecticut, Ohio State (injury issues there too in some of their losses); maybe even Texas, Oklahoma, and UCLA. To be honest the string of upsets opened the door wide open.