The blackened hand again - why not covered?

[Julia]

No: HPFGUIDX 148954

Julie wrote:
[SNIP]
> I think it was significant. An injury that even the WW's greatest  wizard
> can't overcome? That doesn't heal? A dead hand that remains part of
> his living body--because it *can't* be removed and replaced with a
> false hand like Wormtail's, or because Dumbledore doesn't want it
> removed (or covered, which also seems odd)--which is it? Does 
> Dumbledore really enjoy waving that thing around at every  opportunity,
> or is JKR trying to hit us over the head with it?
[SNIP]

As i was reading your post an idea struck me... At first i thought that this blackened hand 
was foreshadowing DD's death, and that its role is only to show us (and Harry) that there is 
not much time left and that those horcruxes are really nasty things to destroy.
But then while reading your post i thought - why did DD even show his injury to anyone 
(except SS and HP)? We see him throughout the book practically showing off his black 
hand! Everybody in the whole school could have noticed that something is wrong with his 
hand - even the Slytherins... What if some student told their parents about DD's blackened 
hand and this information would have reached Voldemort ears (through DEs)? I don't think 
DD wanted Voldemort to know about his injury. It would ruin the whole plan of destroying 
the horcruxes without Voldemort ever knowing it! Surely if Voldemort knew about the 
hand he would also knew how it happened - it was him who put the curse on his horcrux - 
he would recognize the symptoms, he's not that stupid :) 
So here is my question - what was a real purpose of not covering the blackened hand by 
DD?  Is there something we have missed?

Julia