Bindless has nothing to do with UMA and everything to do with the fundamentals of how your GPU accesses memory. Older GPUs had limited register spaces where they could store texture and buffer references, the hardware had no instructions to read textures or buffers outside of the references in those small set of hardware registers. They just weren't able to issue a request to the texture unit to read any old texture, it had to be in that set. The GPU itself wasn't able to update those registers, only the CPU could.

UMA or not doesn't matter, desktop GPUs have MMUs and are perfectly capable of reading the CPUs memory in a unified address space (even back then).