Iirc, in canon, the Gaunt family (Voldemort's family) was the last living set of descendants of Salazar Slytherin, and they were very inbred by the time of the books, so it appears that JKR at least provided some workaround for this.

As for the reliability of Parseltongue, there's some precedent for it apparently serving as truth-enforcement. Chapter 49:

"I am not regisstered," hissed the snake. The dark pits of its eyes stared at Harry. "Animaguss musst be regisstered. Penalty is two yearss imprissonment. Will you keep my ssecret, boy? "

"Yess," hissed Harry. "Would never break promisse."

The snake seemed to hold still, as though in shock, and then began to sway again.

[...]

"You ssay nothing, to no one. Give no ssign of expectancy, none. Undersstand?"

Harry nodded.

"Ansswer in sspeech."

"Yess."

"Will do as I ssaid?"

"Yess."

Professor Quirrell is known for his aversion to unnecessarily redundant conversation, so it seems likely here that he wants to be sure Harry is telling the truth. Later, in Chapter 66:

"Lessson I learned is not to try plotss that would make girl-child friend think I am evil or boy-child friend think I am sstupid," Harry snapped back. He'd been planning a more temporizing response than that, but somehow the words had just slipped out.

It would have helped Quirrell convince Harry in Azkaban, but it's possible he thought it would be more useful for Harry not to know yet how much information his unwittingly-true answers were giving Quirrell.