When you speak of understanding, are you thinking of any particular part of Boom's Taxonomy? Are you using it as a synonym for Comprehension, which is the second step in the Taxonomy, or are you using the term more broadly? When I say "understanding," I use it more broadly, so as to loosely refer to a conjunction of all or some of the steps beyond Knowledge.
Are you claiming that remembering and understanding are sufficient and necessary for each other, even though neither one temporally precedes the other? Regardless, I find this idea intriguing. Would this mean that one cannot occur without the other? If so, then there would be no such thing as rote memorization (defined as "memorization without understanding," where memorization is defined as "committing to memory"). Note that this relates to what Mark Houghton said, which is that "the focus to the debate should be on the little word 'rote,' and not the strawman 'memorization.'"
I think that BEHIND what Art is saying (and behind many of my prior posts on k12.ed.math [on the subject of student solutions manuals and on other subjects]) is this thesis: If what is remembered is sufficiently well-chosen, then understanding can flow naturally from knowledge - understanding can become a natural consequence of possessing some knowledge (that exists in longer term memory and can be held in working memory when recalled). And I believe that this holds regardless of whether this knowledge temporally precedes this understanding.
It's clear to me that "remembering" can be (to a practical degree) scientifically defined and measured. It's also clear to me that "understanding" is not as amenable to a scientific worldview, which is why I (and perhaps others) prefer to focus on Knowledge and let Understanding flow from it. In "Why just about any mathematics is hard to learn," I gave an anecdote of this idea (regarding a struggling 9th grader in Algebra I), so I'm not speaking here in some abstract philosophical way, but hopefully in a way that practicing teachers can find useful.