I would agree. It's amazing how small the world really is. Someone at this place might know someone at your current place.
The interviews that impress me the most are those who can tell the story of what they have done. Don't just talk about the projects but how you solved the problems. Put yourself in the shoes of the person interviewing you and try to think of what problems they face in their role. Try to articulate how you have solved those types of problems before. I have to hire very technical people but I will hire someone with less experience that has a knack for solving needs and a desire to learn and grow.