Snape AK Dumbledore - intimate situation?

[literature_caro]

No: HPFGUIDX 134635

This is something that struck me from the first reading on (I am 
sorry, I haven't got the book with me, so I cannot quote):
In the scene where Dumbledore gets killed by Snape the latter for the 
first time reacts at the headmaster when he is called by him. Snape 
then pushes Draco away and moves to Dumbledore. To me it looks like 
now he is closest to the headmaster. Before killing Dumbledore  Snape 
looks at him for a moment. 
To me this is a very intimate situation and left aside on which side 
Snape is now this seems to be some kind of "fare well"-situation 
which shows that there has been a very intense bond between them and 
Snape is in some way stuck in intense fellings towards Dumbledore and 
knows that this is the last chance to say good bye to this special 
person. 
I know this sounds like saying that Snape is good. But I really want 
to put emphasize on this one: 
If Snape did not feel for Dumbledore in any way but was icy cold on 
the matter of killing him then why did he get so close to him and 
gave Dumbledore the chance to call him for the second time instead of 
clearing him away while still standing in the doorway? I think I am 
right when saying that there is no limit in distance (short 
distance!) when performing the AK. But Snape took the time to create 
a situation in which everybody was excluded from this intimacy and it 
seems to me like he wished that he was on his own with Dumbldore just 
for one moment. 

What do you think about it?

Caro