When we hear Fight or Flight, we envision a choice between dropping everything and running away or an adrenaline fueled charge towards a threat.
It appears to me, under certain conditions, that description does not properly reflect the mental assessment that occurs. Although in reality we do make a choice that boils down to picking between two classes of action, within each class, they are several choices, and exploring that nuance can improve our understanding.
Let's take the situation where someone is confronted by a bully: If your instinctual decision leans towards "flight", there are at least 2 options: run away or submit. If you instinct leans towards "fight", again there are at least 2 options: return the threat of violence in kind, i.e., attack or make it known you will, or manipulate something else in your context as to gain the upper hand.
Often times this relies on manipulating something in the social sphere. One example is utilizing comedy to change the bullies emotional state or relationship towards you. Another is doing something completely weird, thereby affecting the bullies ability to make sense of the situation, triggering their fight or (hopefully) flight response.
Some moves are more ambiguous, however. For instance, when a child calls out for a teacher. It may be seen as a "flight" maneuver, but is actually an attempt to fight. Similarly, submitting may serve as a fight maneuver, i.e., to draw out violence so it can be used against the bully, e.g., showing your bruises to a teacher, etc. Or, for the more Machiavellian, submission may be a means to get close enough to a bully to eventually take them down in some other way.
The point of these examples and analysis is to call into question the nomenclature of Fight vs Flight. It is probably better viewed as "act as if they is no opportunity to gain an upper hand" or "attempt to gain an upper hand."