Rationale:

The standard is clear as written: the stream is read every time operator++ is called, and it is also read either when the iterator is constructed or when operator* is called for the first time. In the example above, exactly two integers are read from cin.

There may be a problem with the interaction between istream_iterator and some STL algorithms, such as find. There are no guarantees about how many times find may invoke operator++.

I do not think the standard specifies what operation(s) on istream iterators trigger input operations. So, for example:

        istream_iterator<int> i(cin);

        int n = *i++;

I do not think it is specified how many integers have been read from cin. The number must be at least 1, of course, but can it be 2? More?