How did Fudge/Snape know about Dementors attacking HP in PoA?

[dorapye]

No: HPFGUIDX 91221


dorapye:
Yikes! Replying to my own post, but I just realised something I 
wanted to add, whihc might all go in with other questions being 
asked by other posters about time travel in the Potterverse.

So, if DD actually *observed* the Dementors descending on H, H and S 
by the edge of the lake, he will also have observed the Patronus.
Later he tells Harry that his Patronus at the Quidditch match 
(final?) when Draco & co pose as Dementors was a stag...
SO, DD would immediately recognise the Patronus as Harry's, 
but..what? There is Harry unconscious by the edge of the lake...DD 
puts two and two together and realises there must be two Harrys out 
by the lake at that moment in time...suddenly Buckbeak's miraculous 
disappearance all makes sense to him too, and he knows what he must 
do....

When DD visits HH in the hospital wing, he knows he must assist them 
in using Hermione's Time-Turner to do what has essentially already 
been done...he knows they are likely to need his prompting and his 
concealment of their time-travelling if he is to convince the 
Minister that Harry and Hermione were not involved in either escapes 
that night.

So, how does this fit, now?
Now I have managed to convince myself, if no one else, that DD, in 
this case at least, does indeed know everything...
 
dorapye