Many years ago, one of our student interns came in bragging how well he had done on his GRE's....He had gotten a 1250, and I was impressed, until he reminded me that that was for 3 parts -- Math, Verbal, and Analytical -- rather than 2. I told him that his scores were on the low end of mediocre. One of his fellow students, with whom I dealt on several occasions, although he did not actually work for us, went to the same school. I did not think he was as bright as Mr. 1250 -- but then his mentor comes in bragging that he got this fellow a graduate assistantship at Columbia. I tried to squeeze out of the mentor and the student what the GRE scores were. All either of them told me was that they were "good."
So no, I don't believe that Columbia has high academic standards at all.