Nexus 5: does it really run stock Android?

Who said it did?

Nexus phones have always had different or at least earlier features than aosp afaik. Further, what is "stock" if not the nexus version? IMO nexus is stock, as it defines what stock is. You could argue aosp is stock but then no manufacturers run stock aosp. Nexus is probably the closest thing you'll find.

Nexus have also traditionally had more of an integrated experience with google, I assumed carriers / manufacturers ripped that out in favour of their own futile attempts.