The two are not independent - it is not a dichotomy.
When I did undergrad level engineering math, I pretty much never had to memorize. Just solve a lot of problems, and it's ingrained in your head. It helped that I utilize that material all over engineering and physics courses. Even now, over a decade since solving problems, I can still recall most of it and use it if needed.
Once I got to upper and grad level math, the approach of simply understanding and solving problems failed me, because you are usually not provided enough problems compared to earlier courses. It may have been good enough for the course to get an A, but not good enough to retain the material beyond the course. I've studied complex variables (Cauchy Goursat, residues, etc) at least 3 times. It's always a breeze, and it's always forgotten soon after. The same with statistics. With the latter, what did finally help me was spaced repetition. Even though it's been a few years since I last reviewed/relearned statistics, I can still read some material involving it and understand it. This is entirely because of those flashcards.
Understanding definitely has to precede memorizing. Insisting that memorizing is a sign of poor understanding, however, is parochial thinking. It's simply not true for the majority of folks.
Statistics and complex variables aren't taught in a way that gives you understanding, they are taught plug and chug. That is why it feels like a breeze and then everyone forgets everything. Basically nobody gets a good understanding for those subjects from taking courses, so you need memorization techniques for them.
Calculus and linear algebra are good examples of courses taught in a way that gives understanding, lots of people understand those after taking the courses, so there you shouldn't use memorization techniques.
So the reason you needed spaced repetition for statistics was that you never understood statistics, you just memorized it, like basically everyone else. It isn't wrong to do that btw, statistics is useful even when you just memorize it which is why it is taught that way, but don't trick yourself into thinking that you really understand the material the same way you did calculus or linear algebra.
When I did undergrad level engineering math, I pretty much never had to memorize. Just solve a lot of problems, and it's ingrained in your head. It helped that I utilize that material all over engineering and physics courses. Even now, over a decade since solving problems, I can still recall most of it and use it if needed.
Once I got to upper and grad level math, the approach of simply understanding and solving problems failed me, because you are usually not provided enough problems compared to earlier courses. It may have been good enough for the course to get an A, but not good enough to retain the material beyond the course. I've studied complex variables (Cauchy Goursat, residues, etc) at least 3 times. It's always a breeze, and it's always forgotten soon after. The same with statistics. With the latter, what did finally help me was spaced repetition. Even though it's been a few years since I last reviewed/relearned statistics, I can still read some material involving it and understand it. This is entirely because of those flashcards.
Understanding definitely has to precede memorizing. Insisting that memorizing is a sign of poor understanding, however, is parochial thinking. It's simply not true for the majority of folks.