Is it true? It's when you design for who you design for. When I see this picture, I think of clients who care about their customers, but they want websites or apps made for them instead of for their customers. I always ask - are you sure? Your clients will really like it? They don't care. Why? Because they treat apps or websites like their children, not products that should make money for them.

Later, is it the designer's fault that the client can't buy something or that the design doesn't meet their needs?

UI is in both cases. What's UX for parents? They need to turn on the melody and make toys run around the circle. Pictures have wrong description. UI for kid? UI is when someone looks at it and sees something. Even it is butt like here. What's UX for a kid? Also, movement of toys and the music. Music can be fun and a good experience.
In this situation, the parents chose the toy for themselves and not for their child.