In principle, a hadith is not an independent source of Deen. Apart from the interpolation in the translation, if we take it as it is, it shows how some women acted upon it. It doesn’t make it necessary that this is the only way to adopt the veil. A veil can be adopted in different ways and the directive is achieved.
However the interpolation in the brackets provide additional meanings. The words of the hadith do not reflect them. The hadith says that on an occasion when some women were not very particular about veil, on hearing the directive hurriedly acted upon it and adopted their veil.
It is not necessary that they covered their faces and whole body with it. There is no mention of covering of faces and the whole body in the narration.
The Arab women usually did not cover their faces that is why when a woman covered her face, it is sometimes mentioned. This mentioning tells that it was not a usual practice.