My take on it is: use grease. Basically for the reasons @ibaldwin states, the BB is low down and gets covered in everything you don’t want it to be covered in especially on mountain bikes.
Torque wise I always make sure that the last “fixing” tension is done pulling upwards with the BB tool so that you can’t put your whole weight behind it in the way that you might be tempted to do if the tool was on the downstroke side of the bracket. Actually easier this way as well since the tool is to the front of the bike not the rear so won’t foul the chainstays.
I’ve not had a BB seize or come loose so if not “right” it’s not wrong!