The important thing here is not the wrapping with a lambda. That's not what made it pure.

The important thing here is the abstract type wrapper. You're exposing pure primitives that are implemented in terms of (hidden) impure ones.

That's why code that uses unsafePerformIO can be pure and referentially transparent, as long as the exposed primitives are pure and implementation details are hidden.

To demonstrate this, imagine that you did expose the PureIO data constructor -- then values of type PureIO would not be referentially transparent anymore.