Actually there is a huge misconception that if you work a job for Disney it gives you some big boost or something. The fact that I worked in one of their restaurants really didn't help me get a job at any other place. It will certainly help if you're trying to get another Disney job but not really for a different part time job. They really don't care
If the person that interviewed you has any idea of the Disney training model it will most certainly help you get a job. Disney packaged their customer service plan and sold the concept to corporations many years ago and MANY large companies use their service model to train their employees. It is a HUGE plus on a resume to have Disney training in your background.