Is it possible to have a fruitless tree grow fruit?

I bought a flowering cherry tree that was supposed to be without the cherries, because I didn't want the mess on the ground. The last two years, I have had cherries come out on it and I am not sure if they are even edible. My kids have tried them and said they are really sour. What is up with that. Can that happen? And can you eat the fruit?
Is it possible to have a fruitless tree grow fruit?
It is possible. The fruitless varieties are cultivated from regular trees, but selectivly bred for their disability to grow fruit. Thats how seed less Ash trees and the like are produced.

The parent trees are fruit bearing to some extent, so your tree won't be completely fruitless.

Another possibility is the tree got mixed up at the grower with another variety. They are all kind of hard to tell apart when they are small.
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