Is the hijaab only for a specific class of women?

Is this true that -- "Honorable or good muslim women wear hajab But low class muslim women don't"? This is the understanding of few muslims in my community. They base their understanding from the following hadith. Please clarify. I'm producing the hadith for your convinience. This hadith is recorded in the Sahih of Al-Bukhari with the following wording: The Companion Anas ibn Malik narrates: The Prophet stayed for three rights between Khaibar and Medina and was married to Safiya. I invited the Muslims to his marriage banquet and there was neither meat nor bread in that banquet but the Prophet ordered Bilal to spread the leather mats on which dates, dried yogurt and butter were put. The Muslims said amongst themselves, "Will she (i.e. Safiya) be one of the mothers of the believers, (i.e. one of the wives of the Prophet ) or just (a lady captive) of what his right-hand possesses?" Some of them said, "If the Prophet makes her observe the veil, then she will be one of the mothers of the believers (i.e. one of the Prophet's wives), and if he does not make her observe the veil, then she will be his lady slave." So when he departed, he made a place for her behind him (on his camel) and made her observe the veil. Few thing I'd like to know more are time frame of this incident, before or after the revelation of Al-Ahzab( 33:59) etc. I'm seeking your opinion as par on-line hadithsearch's recommendation.