I'd go with shnar and Steve on this one.
I believe that there is difference between "Make an attack" and "Take an attack action".
Even the rules that you quoted support this argument:
"A figure’s facing can be changed during its activation
at the beginning or end of an action."
When is the commando active/when does the activation
take place? During the Commando Activation phase, in the order of initiative. Therefore, there is only one active comando at a time. He choses an action and can also change his facing. In this particular example it is undisputably Team Leader. If it were an Interrupt ability, then I would not be so sure, but this is definitely Team Leader's action that allows another commando to shoot
There is, however one exception, as follows in your quote:
"If a commando is allowed to take a move action during another player’s
turn, he can change his facing before or after the move without increasing
his adrenaline at that time."
This case includes "move action
", whereas the former only talks about "ranged attack".
The next paragraph "When a commando performs an attack action,..." talks about "attack action
" taken by the active commando during the Commando activation phase, this beeing again Team Leader.