Most vexing parse

I got the code from here.

class Timer {
 public:
  Timer();
};

class TimeKeeper {
 public:
  TimeKeeper(const Timer& t);

  int get_time()
  {
      return 1;
  }
};

int main() {
  TimeKeeper time_keeper(Timer());
  return time_keeper.get_time();
}

From the looks of it, it should get compile error due to the line:

TimeKeeper time_keeper(Timer());

But it only happens if return time_keeper.get_time(); is present.

Why would this line even matter, the compiler would spot ambiguity on time_keeper(Timer() ) construction.