You are right, guys, the "Valet" button allows a valet parking attendant to open the car body but not boot or glove box (you did lock it, didn't you?!) and drive the car, using the green-topped key.
I had to park in central London, a couple of weeks ago. The nearest car park (£17 for 3 hours) ended up being operated on the valet principle. Guess what? I don't have a green topped key - probably the first owner thought "Don't need this, we don't have valet parking in the UK" and chucked it.
Nevertheless, I gave the parking attendant the full set of keys and he returned the car all complete and without anything added or missing in the boot.
Guess we trust our chaps more than they do in the good old US.
BTW the company had to pick up the tab for the parking but it was STILL cheaper than going by train, even after I had paid "Red Ken's" congestion charge! I could have had the car veleted, as well, but you have to pay the guys more money, not just press the valet button twice!