I would like to thank you for giving me a good laugh today Cyiwin. So the crisis you are facing basically is this: You want no-one to have the ability to see what you pull so you can safely hoard all items, regardless of its usefulness to you or not without being called on it, but yet you also still want full ability to covet anything the rest of the party pulls in case you see something useful to you so you can ask or roll for it?
Congrats on making my list as a living definition of narcissism.
*EDITE*
And I firmly belive that whatever is in the chest is yours to decide what to do with, unless as other posters have said that when you joined the party you are told otherwise by the leader in which case it is your choice to run with them or not under their rules.
Now this being said, most sane people when pulling something that is of absolutely no use to them will put it up for roll. Some will loot everything anyways, and this is fully their right, but it is also fully the right of the rest of the party to know that the person they are running with does this. And then can choose if they wish to run with this person again in the future or not. Personally I would perfer running with someone familiar with the concept of sharing.
This system has worked perfectly well for years, I see no need for "hide my loot" as a choice ingame, except for the exceptionally greedy players who do not want to be called on or excluded for their self-centered, self-serving behavior ingame.
Kit