What are you guys calling work responsibilities? My parents basically told me the same thing - I'm not going to sit around on the couch all summer so I had to either get a job or play sports. Obviously I chose baseball and then football when it started. Now I still had "chores" I had to do regardless of the fact I was doing baseball and football. It was still my responsibility to cut the grass, help wash dishes, clean the house if mom said so - whatever. They gave me an allowance to help learn to budget money and learn the value of money.
This strategy may not work with everyone and that's fine. Each set of parents have to find what works for their kid and that may change with each kid because my sister went out and got a job. But she still had her chores around the house and my parents still controlled her money to learn the value and budget of money.