I really wish we would add the step to check the regulator dial for cracks and point it away from us and the PT before turning on the bottle. Unfortunately, we've had some minor injuries occur when the valve dial is old or broken and that clear plastic cap shoots off. It's already a step we include for scuba diving as well for the same reason (although MUCH higher pressure in a scuba tank).
This is an instructional video going over the process on the exam, to prepare those for what they should expect. I highly doubt this person was being tested.
I personally wouldn't want it slipping off the back off the head and smacking the patient in the forehead or something like that so I'd pull it down further as long as you're careful with the head movement depending on the situation
in this situation it would be fine since there is no need for spinal immobilization but sometimes when they require a cervical collar you arent really able to pull it down much without compromising their spinal stability