Depending on how you view 'pure' blood, the very act of producing a child with a muggle would be enough to 'taint' the line.  That, at any rate, would fit most known interpretations of such matters...a half-blood would be more tolerated, but only just.  Therefore, there's probably a workaround or 'gentle-wizard's agreement' somewhere.<br/><br/>And now you know why Vincent keeps a low profile.