Is g++ -Wdangling-reference warning justified in this case?

Compiling my code with gcc 13.2 and -Wdangling-reference I was surprised that in this simple scenario (godbolt):

#include <vector>
#include <string>

std::string& add_variable(std::vector<std::string>& vars, const std::string& var)
   {
    vars.push_back( var );
    return vars.back();
   }

int main()
{
    std::vector<std::string> vars;
    const std::string& var = add_variable(vars, "name");
}

The compiler warns that:

<source>:13:41: warning: possibly dangling reference to a temporary [-Wdangling-reference]
   13 |     const std::string& var = add_variable(vars, "name");
      |                        ^~~
<source>:13:59: note: the temporary was destroyed at the end of the full expression 'add_variable(vars, std::__cxx11::basic_string<char>(((const char*)"name"), std::allocator<char>()))'
   13 |     const std::string& var = add_variable(vars, "name");
      | 

Is this a false positive or there's something big I'm missing here?

Indeed, it looks like a false positive. var is referencing the std::string in your vector<string> which is still very much alive after the full expression.