Davies, who is heading for a Wembley final with Swansea in the Capital One Cup this month, impressed Williams when he turned up in an unfashionable car.
"The boys were saying we liked that because you get some of the other young players driving a Mercedes and they haven't played any games yet.
"But that showed us Ben was grounded. It was a little red VW Polo. Now he has just got a new one, but even then it's a little Audi.
"He hasn't gone too far over the top. He wants to play football and do well at it, rather than be obsessed by any of the things that come with it."