Trelawney and ignorance

[Inge]

No: HPFGUIDX 96325

GOF - uk edition - pg 177 - Trelawney to Harry: " .....I think I am 
right in saying, my dear, that you were born in mid-winter?"
"No," said Harry. "I was born in July."

What's this about?

1) Trelawney doesn't know who Harry IS (the boy who lived)? Has 
Dumbledore - for whatever reason? - kept Trelawney inside Hogwarts 
since he first hired her (before Harry's birth) and kept her ignorant 
of the Harry/Voldemort incident? 
If she knows the story about Harry isn't it sort of weird that she 
doesn't know when he was born? He IS - after all - rather famous!

2) Could it be that Trelawney was actually *right* about Harry being 
born in mid-winter? In this case - what does that mean to the story? 
And why would somebody (Dumbledore ?) lie about Harry's birthdate? To 
keep someones (Voldemorts ?) attention away from someone else 
(Neville ?).

This has probably been talked about before - but Trelawneys ignorance 
on the issue of Harry's birthday confuses me.
Theories?

Inge