If you don't trust the dental clinic, then get a second opinion. You could also ask the clinic to point out the cavities on the x-rays.
However, it is certainly possible for kids to have that many cavities, especially if they haven't been getting regular dental care. It sounds like their parents are doing the right things, but if they were falling asleep sucking a bottle earlier on or if they don't brush regularly or whatever, they could have a mouthful of cavities.