Dumbledore and the Buckbeak execution

[Inge]

No: HPFGUIDX 131874

As everyone else I'm going through books 1-5 to get shaped for HBP :-)
And since it's been a very long time since I last had a chance to visit 
this wonderful group, I simply gave up trying to find out - in the 
archive - if this question has resently been brought up.
It's not even a real question because nobody but JKR has the answer - 
it's more like a "what do you think?"-sort-of-thing.

Book 3 (POA Bloomsbury Paperback p. 288 "Hermione's Secret"):

Dumbledore: "......If all goes well, you will be able to save more than 
one innocent life tonight........"

My question (which, Im sure, has been asked before, sorry) is, why did 
he say that? Dumbledore was present at Hagrid's when the execution of 
Buckbeak was supposed to take place and he knew already that Buckbeak 
had left the scene and was safe by the time he visited Harry and 
Hermione in the hospital wing. But since he said what he said, he must 
also have known the first time around that H & H were timeturning and 
that they were present in timeturning-form when he visited Hagrid's hut 
along with Fudge and McNair.
How on earth did he know that?

Inge