That's a very arrogant and foolish thing to say. Their understanding of the material probably far exceeds yours, and I bet they could reproduce any of those derivations without much trouble. It is clear that you value memorization highly, but understanding is far more important.
I bet your wrong. I am not saying I could reproduce the derivations either ... I am not sure why you think that was arrogant or foolish. It was my assessment of their understanding.
I am also not saying I value memorization. In fact, I hated the biology and organic chemistry classes that relied so much on memorization. When you understand something like electromagnetism or classical mechanics really well, you can basically just remember the main ideas of a derivation and the details will follow. When you understand the subject poorly, you need to recall all the details to complete the derivation.