No. You woke up. You had a weapon in your hand. He did not have the opportunity to just stab you through the eye when you slept.
Which is stupid too as it implies every character wakes up in time.
In any case, the game never tries to call infiltrators assassins. That's all the players' doing. Just like trying to make them out to be ninjas.
The official help page on classes states that infiltrators may be able to:
carry out assassinations
and those who assassinate are assassins. Also, the ninja thing is based on all the descriptions of the class including the name, supporting ninja like actions.
