Parabellum is right.
The whole system of priority baggage has been diluted somewhat since the introduction of ULDs. It is difficult to allocate the priority baggage to the correct container, because it may not be full, and thus have to be positioned differently on the aircraft in order to comply with the weight and balance requirements, and thus may not be the first container off the aircraft at destination.
Final 3 greens is also correct. If baggage has to be sacrificed in order to increase the fuel load (a more common occurrence than you might imagine), then the priority tag carries some weight (if you'll pardon the pun!).
On non-containerised aircraft, it's basically down to the loading crew. If they're feeling a bit bolshie, priority bags will go in first, and likely as not end up on the last dolly which trundles to the terminal. It's a lottery!