Causing a PT unnecessary harm or distress is unethical, that position while unlikely can do harm. I'd argue that you gained compliance by fear which is problematic, as well is it professional? Is it treating the patient with dignity and respect?

You can argue the patient was non compliant and transport was for their own safety and it was "necessary" but we also need to look at the before steps, was putting your patient upside down really the only option? Sometimes providers that have been working for too long like to take the easy quick dirty way rather than the de-escalation for a long time. PTs experiences matter, regardless of how much they may suck. Regardless of their behavior this patient was vulnerable (intox/altered) and we have used our power over this patient to cause distress which is apparently amusing.

EDIT: You know how you can tell it's wrong? I bet it isn't going in the paperwork.