Yes, Amartya Sen does seem to project modern ideas of what a university is on to what must have been a very different sort of institution, and it spoils the case he is defending.

It's not the first time that he has claimed a specious continuity with ancient Indian culture. In a book whose title I forget, he makes great play with the terms nyaya and niti, as if they were etymologically related, but without indicating how they are used in Sanskrit literature, or anchoring his use of them in any earlier use. I was impressed by his arguments on economics and ethics, but thought they were let down by his apparent assumption that because he is Indian his ideas ought to have Indian roots, or be made to look as if they have. I was reminded of the remark of another argumentative Bengali, the historian Romesh Chandra Majumdar: "In a democratic age, everyone seems to assume that a knowledge of Indian history is a birthright of every Indian, and requires no patient study or research" (in Historians of India, Pakistan and Ceylon, ed. C. H. Philips, p. 426).

In a somewhat different vein than the ongoing discussion of a certain Hindutva partisan, you might want to take a look at Amartya Sen's piece: http://www.nybooks.com/articles/archives/2015/aug/13/india-stormy-revival-nalanda-university/

In my opinion, while his political position seems to be something close to 180 degrees the opposite, he is in some ways remarkably similar in his almost studied ignorance of classical India. His portrayal of Nalanda is nothing short of fantasy, and I confess that I am disappointed and depressed to see such fictions repeated by someone who, until recently, was actually significantly influential in this 'neo' Nalanda project. That it might be advantageous to say certain rosy things in a political context is one thing, but the result is, to my mind, an utter misrepresentation of the historical truth. A final point is that by portraying Nalanda as an international university, using in his description explicitly secular categories, the anti-Hindutva Sen succeeds in virtually entirely subverting the Buddhist nature of Nalanda.