User interface design can be UX design if you utilize an iterative user-centered design approach, because that is very much an evolving approach that specifically targets the user. It’s a process that’s intended to take into account the user experience/usability, and directed at helping the user achieve their desired goals of the software. There’s user research involved to create and reach the end product. I just don’t think you can make a blanket statement that UX design isn’t UI design.