Usually its in work time plus the time it takes you to drive to work. If it took 3 hours to drive to the course usually you'd be put up in a nearby hotel at least out of courtesy to the organiser so you dont turn up 1 hour later when getting stuck in traffic.
We use to have an individual who refused to attend courses, couldnt leave his cats. The only problem is you end up the dogsbody not trained on anything.
As for the PM's any manager factoring 100% of your time should probably not be a manager. I was always told someone working fulltime should only be factored as 0.8 wte. This takes into account an acceptable amount of sickness, training, admin and any other unaccountable events.