Why are they looking for new care I would weary in that I would think the parents know what to say to get you to sign them on. If they realize you are firm on naps they will possibly act as if they are all for naps...then let you tough it out and realize the kid just doesn`t nap.
If you did plan to move ahead I would expect a good amount of effort on your part...especially if it is true that the child stopped napping when they switched from playpen to mat. This seems to imply the child isn`t disciplined to staying on the mat as I see no other reason for this to be the reason for naps to end.