I finally asked what they were so concerned about and they revealed that they thought I might be "too nice" for the position. So after explaining some toughness (perhaps by getting assertive and asking what they were getting at), I was able to reassure them that I don't let things get to me, that I have clear boundaries from the start, and that I can hold my own. Basically, I needed to reassure them that I wouldn't crumble - and we moved on.