Your quote didn't and doesn't mention sati 'attains' purity there i.e. it is developed there, rather 'it is pure there' there is a difference, and I am not doubting it is pure in the instance you quoted, what I am doubting is it is developed there, rather than due to causes and conditions of the other folds.
As there are Suttas (i.e. the teachings) which refer to right view being required for sammasamadhi and the other folds of the path also, is it to be assumed they are all sammasamadhi under different guises? no, that would be taking the part of the teachings out of the wider context of the other teachings and because the deeper levels of concentration are not required for liberation (only certain knowledges/powers) it is pushing sati out of its wider context within the teachings also.
You asked a question and it has been answered, what are you trying to prove?
He who knows only his own side of the case knows little of that. His reasons may be good, and no one may have been able to refute them.
But if he is equally unable to refute the reasons on the opposite side, if he does not so much as know what they are, he has no ground for preferring either opinion …
He must be able to hear them from persons who actually believe them … he must know them in their most plausible and persuasive form.