Harry's Pureblood Status

[Trina]

No: HPFGUIDX 12541

Hi all!  

I am in the middle of a GoF re-read and just finished Chapter 24, 
Rita Skeeter's Scoop.  At the end of the chapter, Hagrid is telling 
Harry, Ron, and Hermione about his mum and he says this:

"Yeh know what I'd love, Harry? I'd love yeh ter win, I really would. 
It would show 'em all...yeh don' have ter be *pureblood* ter do it.  
Yeh don have ter be ashamed of who yeh are."  (the italics are mine)

Woah!  I assumed that since Harry's mum and dad were a witch and 
wizard, Harry *was* a pureblood.  I know Lily was Muggle-born, but 
still, I didn't think that would qualify him as not "pureblood".  
When Malfoy uses the term Mudblood, he only aims it towards Hermione 
a full-blown Muggle-born, not Harry.  

Not that Harry's "pureblood" status matters one whit to me, I'd love 
him anyway, but I was confused by this discovery.  So, what do y'all 
think?

Trina