another LV - Riddle question

[Blackness]

No: HPFGUIDX 98906

Lynette:
<snip>
> As to why SS recognized TR as his true heir - he could speak 
> parseltongue, he studied the dark arts for years, he agreed with 
> the no mud-bloods (even though he was a half blood), and he cared 
> enough to try to find the chamber for years.  His hatred of his 
> muggle father increased his hatred of the mud-bloods. The magic 
> that SS left to protect the chamber recognized this kindred of 
> spirit in TR.


Gina: 
    Okay let me clarify - I know it is possible Tom could be related 
"heir" of Slytherin, but why would SS RECOGNIZE a mudblood as his heir? 
Does that make more sense? Yes, they could be related, but why would 
Slytherin condone this mudblood messing up the perfectly pure family 
tree?

I have a theory about this.  Slytherin's "Heir" was often referred to 
in the singular.  There is no other mention of the Chamber ever being 
opened other than Riddle Jr's time in school and revisiting of Hogwarts 
via his diary in Harry's time - Dumbledore was adamant in the hosp wing 
that it WAS Voldemort responsible then too, even before it was made known.

What if - all the Slytherin descendents were female until Tom Riddle Jnr?  
And the missing ingredient all that time was Muggle blood, because being pureblood fanatics the females refused to intermarry?