I mean the guy has a PhD in mathematics so I'm sure he understands his tools deeply. Certainly more deeply than I did when I was an undergraduate in his class. Sometimes the right analogy, even if imperfect, is more helpful to build intuition than pages of rigorous proofs. Chill out.
Of course maths need intuition, it isn’t always incompatible with being rigorous
But yes some who have PhD in physics don’t always care about understanding deeply maths tools. Depends what you’re doing