Current astrophysical data shows that the large-scale spatial geometry of our universe is flat, meaning parallel lines remain parallel and triangles add up to 180°. However, flatness does not strictly prove the universe is infinite; a flat, simply connected universe is mathematically infinite, but a flat, multiply connected universe (like a cylinder or a hyper-torus) could be finite.Observations of the Cosmic Microwave Background have measured this geometry with incredible precision, though slight margins for error still allow for the possibility that the universe curves on scales far larger than what we can observe.Whether the universe is finite or infinite remains an unresolved question in physics, though scientists generally use an infinite, flat model for standard cosmological calculations because it is mathematically simpler.

He isn't wrong. With the assumption of homogenous infinite universe, basically everything is guaranteed to happen somewhere.

Edit: For your pefect copy alone you don't even need an infinite universe. Just one big enough for that to randomly happen.