OoP: Pureblood Relations - what about the Potters?

[eay50]

No: HPFGUIDX 66650

Okay, this has been troubling me since I first read the tapestry 
scene.

Sirius says that pretty much all pureblood wizards are related 
somehow.  If that's true, why doesn't he mention the Potters??

We have been told again and again that Harry is 'half-blood like 
Voldemort' - that Lily was muggle-born and that James came from a 
wizarding family.

If Sirius went to all the trouble of telling Harry about his distant 
connections with Molly and Arthur, why would he not mention Harry's 
own family???

Any suggestions?

E.A.Y.