Well, I must say that they are obviously mistaken!
The only relation between both is that UX might be a result of UI but not necessarily, we can achieve UX even when there’s no UI at all!
UX is about user feelings and perceptions.
UI is about interaction controls for the user.
Who is the UI Designer?
He is the person who has the talent to create elegant interface elements to appeal the user.
Practically, his role is about shape and color, and it is a unique criteria, requires long experience and large amount of time to satisfy various tastes.
His tools should be freehand sketching and digital design software like Photoshop and Illustrator.
Unlike the UX Designer, who has the knowledge of human psychology in terms of reactions and responses to designs, his role is about defending the user rights and controlling user perceptions for designs (specifications, user scenarios, wireframes, ..,etc).
His tools are the same as UI Designer in addition to OmniGraffle, Axure, .., etc.
Unfortunately, some employers not just treating UX Designer as UI Designer, they also require a full set of skills in scripting and mark-up languages in order to develop the actual UI interfaces, much like they combine UX Designer, UI Designer, and UI Developer in one role! sometimes they even require much more technical skills like advanced server scripting languages like PHP, Perl, .NET, ..,etc!
I am in fact one person who do believe that each UX Designer should have background about technologies and development, it helps to fully understand how to implement certain designs according to the latest available technologies ..
But not to do the whole task starting from conceptualization going through design and ending with final interactive product! it’s simply a huge waste of time and much higher expectations from a single talented person ..
It would be more efficient if the UX Designer works closely with Marketing Directors, Information Architects, and Creative Directors ..
It’s about time to emphasize the business needs by satisfying the actual users, the global competition went too high due to the wide production for different designs, the users are increasingly get lost and that affects business needs for sure ..
Related articles about wider perceptions that covers this subject: