Can every μ-recursive function be defined using a single instance of the μ operator applied to a primitive recursive function?
According to Wikipedia, any μ-recursive function can be expressed as the μ-operator over a primitive recursive function (source):
A consequence of this result is that any μ-recursive function can be defined using a single instance of the μ operator applied to a (total) primitive recursive function.
From this I conclude that given a μ-recursive function $f(x_1,\ldots,x_n)$, I can write it as $\mu y.R(x_1,\ldots,x_n,y)$ with $R$ being a primitive recursive function.
If so, let's say there's a function $h(x,y)$ which is μ-recursive but not primitive recursive and its range is $0,1$. As $h$ is μ-recursive, then I can write it as $\mu z.R(x,y,z)$ for some $R$ primitive recursive. However, as $h$'s range is bounded, the 1-bounded μ-recursive operator (which is primitive recursive) over $R$ should give us $h$ as primitive recursive. Absurd! Regarding the existence of $h$, in this review they show how to construct one of these if I understand correctly.
The question, then, is: what am I misunderstanding in Wikipedia's remark?
Final note: this seems to be an example in Kleene's book Introduction to metamathematics (§58), but I don't see how it is solved.