"Noble and Most Ancient House" is usually only prepended to "Black", in canon or fan works. There are few enough wizards that I would believe all purebloods can use that sort of distinction, and for someone to actually be concerned with their own blood purity they should have records that invariably would link them to several prominent houses if you went back far enough.
So it doesn't strike me as odd that "pure blood" is equated with "noble house".
The Weasleys are canonically pure bloods, but "class traitors," and so do not associate much with other pure bloods, but I don't think they were ever meant to be a noble house.
I think "pure blood" was only meant to imply that a person can trace their heritage back a long way exclusively through people who were witches and wizards, but this doesn't mean that they necessarily ever held a position of nobility. To paraphrase something from one of Terry Pratchett's books, "The Vimes name goes back a long way, but so does the name Smith...
Warning: As per the official spoiler policy, the following discussion may contain unmarked spoilers for up to the current chapter of the Methods of Rationality. Proceed at your own risk.
Assume HPMOR was written by a super-intelligence implementing the CEV of Eliezer Yudkowsky and assorted literary critics. What would it have written differently?
... is what I want to know, but that's hard to answer. So here's an easier question:
In what ways do you think Eliezer's characterisations/world-building/plot-fu are sub-optimal? <optional> How could they be made less sub-optimal? </optional>
(My own ideas are in the comments.)
To put it another way... Assume a group of intrepid fanfic writers in the late 2020s are planning to write a reboot. What parts of Eliezer's story do you think they should tweak?
And just to make sure we're all on the same page: Eliezer isn't going to go back and change anything he's written to bring it in line with anything suggested here. This is purely an "Ah, just consider the possibilities!" thread.
... which means that we can safely suggest drastic rewrites encompassing 30 chapters or something. Or change fundamental facts about the world.
(Exercise due restraint on this one. Getting rid of the Ministry/the Noble Houses/blood purism would probably turn the story into something completely different; this isn't what we're trying to do here.)
With that, let the nit-picking begin!!