I'm in a heated debate in which case
Is there strategy in FPS.
&
There isn't a need for strategy in FPS if you have good "twitch mechanics"
It depends on the FPS
If I switch my loadout in Battlefield 3 to incorporate smoke launcher, then yes, I am strategizing for my team and planning advances. If I'm loaded out with HE Launcher and just fragging everything in sight, that's just skill and twitch gaming.
In Counterstrike and CS:Source clan matches, 100% Strategy in needing to coordinate nade throws / smoke / flashes / and rushes. If one sides timing is off and they catch a flashbang in the face while rounding the corner then it can cost them the round.
Calling out when to fall back and regroup to attack a different bombsight or calling a fake push is all strategizing by the team leader.