The whole assertion of "understanding how a proof is done rather than memorizing it is how maths should be done" holds true, BUT only when you are not bound by time or a deadline, which is not the case most of time, whether you are working through a test, an exam or even on a PhD, you cannot afford losing time "reinventing the wheel"; working on proving theorems that have already been proven rather than using them directly.
The factor of time forces you to "memorize" certain concepts/theorems/facts so that you can use them directly as tools.
Personally, my approach consists in working on proving these "tools" at a first stage; understanding why they are true, then, I simply go past that and simply "memorize" them in order to boost my workflow.
In a nutshell, in order to be productive (doing maths or even physics), you must memorize shit, just don't do it blindly.