I believe the use of "fairness" should be used with equal stats (health/shield, etc.) all else held constant (equal skill, guns, etc.). The system of health packs breaks this flow. As you mentioned of someone making the decision to challenge and win a gunfight. This means you are stuck with less health for the next engagement, which breaks the "fairness" for the next encounter.
And so do different weapons, different positions, and different shield states (by the definition you provided). So what's your point?
This could lead to players with higher skill losing to objectively worse players because of an imbalance between the two.
Again, so could the three other attributes I have mentioned multiple times. But we're all okay with that.
The reality is, it happens. People lose encounters to opponents who are worse than them all the time, because the worse player has an advantage. And this phenomenon happens in every well designed game ever, because in a well designed game a realistic player cannot predict every action of their opponents, which will mean that a worse player will sometimes perform better than the better player. It is not, in any way or form, a flaw in the design. It is a simple consequence of the fact that real players do not play optimally.
This begs the question of when the game should be equal and when not to be.
In general: the game should give equal chances for every player to succeed when the match starts. Then there's the arena shooter paradigm of symmetric spawns. However, after the game starts the decisions of players will inevitably lead to an inequal game state. This is natural, and should not be fought. What's more important is to ensure that the inequality doesn't remain static or become runaway, i.e., that the victory isn't too strongly influenced by which team gains control at the beginning of the game.