From other aspect, he may be right. Say if we create a bitmap whose length is 2^64-1(constant, O(1) space with respect to n), and use it as a hashmap...

From mathematical perspective, the space complexity of such solution increases linearly as the length of the array grows, no matter what space unit it is - 1 bit or 8 byte.

Do you think the bitmap need O(n) space? We need to represent the nums from 1 to n.Although the bit map could reduce the space we use , it remains O(n).