I have no idea what the author has in mind, but their statement is wrong from the beginning: somatic motor activity is _not_ always voluntary. Reflexes are a good and obvious example.
"Fight or flight" response is basically half of the entire ANS (the sympathetic part), so that's incredibly broad. Parts of that response are definitely involuntary.
I think it's more likely that Wikipedia is thinking of things like breathing, which is normally under ANS but you can also manually control your breathing. They may also be thinking of things you can do to directly influence your autonomic responses, for example, if you start running, you are voluntarily moving your muscles, but the autonomic nervous system will also participate (for example, by increasing your heart and breathing rates).