Cannot match rvalue reference function with GCC

When attempting to use an rvalue reference, I get the following error from GCC (clang does not generate an error):

/usr/include/c++/8/istream:951:12: error: no match for ‘operator>>’ (operand types are ‘std::basic_istream<char>’ and ‘std::basic_istream<char>& (*)(std::basic_istream<char>&, std::__cxx11::basic_string<char>&)’)

The code I am trying to compile is:

typedef std::istream &getline_type(std::istream &, std::string &);

void operator>>(std::istream &, getline_type) {}   // 1
void operator>>(std::istream &&, getline_type) {}

int main()
{
    std::string s;
    getline_type *getline = std::getline;          // 2
    //using std::getline;                          // 3
    std::istringstream("a") >> getline;
}

If I comment out the line marked // 1, it works.

If I use the line marked // 3 instead of // 2, it also works.

Why is the compiler generating an error? Is it a bug in GCC?

I believe clang is correctly assessing that the code is well-formed, but if there is a valid reason to reject the code, it might indicate a bug in clang.

Try it online!