Another similar issue to the operator< vs greater in nth_element but not as direct occurs in [alg.heap.operations]:

-1- A heap is a particular organization of elements in a range between two random access iterators [a,b). Its two key properties are:

1. There is no element greater than *a in the range and
2. *a may be removed by pop_heap(), or a new element added by push_heap(), in O(log(N)) time.

As noted by Richard Smith, it seems that the first bullet should read:

*a is not less than any element in the range

Even better the heap condition could be stated here directly, instead of leaving it unspecified, i.e.,

Each element at (a+2*i+1) and (a+2*i+2) is less than the element at (a+i), if those elements exist, for i>=0.

But may be that was may be intentional to allow other heap organizations?

See also follow-up discussion of c++std-lib-32780.