You don't need to be Hermione to read or ask about the school you're going to. Isn't this supposed to be part of being a "good Slytherin"?

Harry had Draco, Ron and Hagrid before he arrived at Hogwarts. There's a big chance that on the way a random muggleborn will hear about Slytherin's reputation. Or just have the hat tell him "you have qualities that fit Slytherin, but you wouldn't necessarily fit there".

In any case, a muggleborn certainly won't profit from being sorted into Slytherin, which was the claim I was arguing with.

 

From Harry Potter and the Deathly Hallows: Chapter 23

This imply that there are in fact muggleborns in Slytherin but not a lot.

 

When Harry says that he and his friends are from Slytherin. Greyback laguhs ans says something along the lines of: "That's what they all think we want hear." Which implies that the death eaters and Voldemort don't care about what house you are/where in, just how pure your blood is.

 

Debatable. It can also be viewed as a rhetorical question pointing out that that there are none.