An easy way out for the murderers
-spoilers alert-
I wonder how they did not think of it. When Rupert calls - as if to come up and search for his 'forgotten' cigarette case and Philip becomes panic stricken - they should have thought right away that he is coming back to actually open the chest. They know he was asking questions. And Brandon should have remembered how Rupert wanted to help the maid with the books - not because he is polite and everything of course - but because he was sniffing something.
An easy way out of this would be to attach a bit of 'magic trick' the way magicians do the most obvious. Simply move the corpse in the closet or in the other room or wherever before Rupert came up the stairs.
That way they could continue to play guilty and strengthen Rupert's suspicion. And then reluctantly open the chest and show him it is empty. Then Rupert would think to himself "I am going mad, what was I thinking, there's nothing here" and all suspicions would be cleared. It is an ideal way to seal Philip and Brandon's alibi even more firmly. But panic on one hand and undermining on the other are never a good adviser.
On second thought being stupid enough to leave David's hat in the closet for everyone to see I think it would have been quite improbable for them to manage to think of this way out. So, again a clever concept by Mr. Hitchcock and well deserved finish.