Yes, a CLI CAN be turing complete and a GUI cannot be.
No, you're wrong. Just because *most* GUIs are not Turing complete doesn't mean they can't be. Informal proof: Take a Turing complete text-based language, convert the keywords, structures, operators, constants, variables etc. into GUI editable objects, write a GUI that allows these objects to be assembled in arbitrary ways, e.g. by drag-and-drop, and there you go. Effectively you are visually constructing some sort of flowchart which is mathematically equivalent to a textually expressed program. Some GUI IDEs are actually like this, which shows that the principle is possible in practice.
You might object that such a GUI IDE is not Turing complete on the grounds that it can't do this or that function with the underlying hardware/low-level OS etc.. but that's not valid; a general Turing complete language does not have to have access to lower levels of software/hardware. A concrete example is that many 'normal' text based Turing complete languages might not be able to do direct I/O or access raw devices of any sort, or handle DMA or interrupts, and thus might be unable to perform certain functions (like read the disc partition table for example) without invoking routines in some *other* (lower level) Turing complete language. But that's not what Turing completeness is about; it's about being able to express an arbitrary algorithm on an abstract machine.
Doing this through a GUI may be clumsy in many cases but not impossible.