Harvard certainly believes this. And if Dean Khurana were being fully honest about it, he would have said that, in fact, from Harvard’s perspective, there are many more applicants to Harvard with attractive characteristics than can be admitted, and the idea that anyone “deserves” to go to Harvard is misplaced, for more complex reasons than those he cited.
Harvard, a private university that constantly seeks to do more and more of what it does (teaching and research), and expand its reach and power as much as it can, admits - as is its right - about 2,000 students to Harvard College every year in the belief that this is the group best-placed to help Harvard achieve these goals by virtue of each individual’s attributes, which may include brilliance, special talent such as the ability to throw a ball well, your family’s wealth, the state in which you reside, your racial/ethnic background and a thousand other things.
Just because you’re “qualified” to go to Harvard (which means you’d be able to graduate) doesn’t mean you “deserve” to be admitted. If Harvard offered you a spot, you “deserve” it, insofar as the term is applicable. If they didn’t, you don’t (even if Harvard made a mistake and it would have been better for them to have admitted you than someone else who got a spot).
Dean Khurana fully understands this, of course, but can’t say it out loud. It suits him to throw it back on the students and tell them, in effect, to check their privilege, rather than acknowledge his important role in perpetuating a system that anoints ~2,000 kids each year for the purpose of advancing the institutional goals of Harvard. It’s worth noting that even though those goals produce positive effects by increasing human knowledge and promoting teaching, they also benefit Harvard and its stakeholders monetarily and otherwise.
Instead of telling these students that a lot of what they’ve achieved is due to luck and they should be more humble, and leaving it at that, it might have been instructive for Dean Khurana to add that he, and Harvard, are also very fortunate for many reasons, including the ability to pick and choose each year the group of students that will be most useful as tools to make him and Harvard, the richest and most powerful university in the world, even richer and more powerful.