It's not like he actually feels possessive or even protective of anything in this room. As far as he knows, he doesn't have any possessions here. What Leon does have an issue with is someone whose poking through other people's things with the intention of stealing them. Just because he doesn't have shit to steal doesn't make it okay.

But then the stranger actually gives him an explanation.

"Out of place? How would you know if it's out of place?" Leon peers down the hallway in both directions, watching out for orderlies, before stepping inside and closing the door to give them some privacy.

"I don't really remember getting here. I just sort of... woke up a while ago."