This is described elsewhere on Pottermore under the heading "The Potter Family":
Potter is a not uncommon Muggle surname, and the family did not make
the so-called ‘Sacred Twenty-Eight’ for this reason; the anonymous
compiler of that supposedly definitive list of pure-bloods suspected
that they had sprung from what he considered to be tainted blood.
There's also the fact that it's explicitly noted that the family is not actually pure-blooded at all, with numerous inter-marriages with muggles:
The Potters continued to marry their neighbours, occasionally Muggles,
and to live in the West of England, for several generations, each one
adding to the family coffers by their hard work and, it must be said,
by the quiet brand of ingenuity that had characterised their forebear,
As Hagrid points out in the Chamber of Secrets film, the concept of 'pure-bloodedness' is a complete nonsense anyway.
Hagrid: "And it's codswallop, to boot. 'Dirty blood.' Why, there isn’t a wizard alive today that’s not half-blood or less."