No, it's not equivalent. Reducing cognitive load includes (in particular) the elimination of extraneous, non-germane, or duplicate information or tasks.
A specific example that the paper gives is filling out long forms; if you can replace a long form with a shorter one, that is a reduction in cognitive load and bureaucracy, but it is not "dumbing down" anything.
I'm not so much editorializing but translating to common speech.
I stand by it. That's pretty much what they were saying.