PSU still broken?

They will not fulfil more than one requirement per staff member, but if all of your staff are trained in Lvl 1 & 2 then once enough have fulfilled Lvl 2, the rest will count towards Lvl 1 etc, which is accurate to real life as you would not have a medic dual role sgt who is Level 1 and 2 as they have very specific jobs on scene. It is not a bug. You just need more staff in general. Having said that, there is nothing stopping you from training staff in as many different skills as you like.