The Hadith in reference is quoted in Bukhari. The Sahaba, Radi-Allahu anhum, enquired from Rasulullah about the meat slaughtered by the A’araab (Muslims living in the outskirts). Since they have recently accepted Islam and the Sahaba, Radi-Allahu anhum, did not witness the slaughtering and the Tasmiyah (reciting of Bismillah) during the slaughter, that created a doubt in them.
Upon that, Rasulullah said, "You say Bismillah and eat the meat." In other words, you do what you are supposed to do, that is, recite Bismillah before eating and do not have a baseless doubt as the animal is slaughtered by Muslims who must have recited Tasmiyah before slaughtering. The order to recite Bismillah and eat was not as a substitute for the Bismillah at the time of slaughtering. (Fathul Bari; Ibn Hajar)
It is not permissible to purchase meat from non-Muslim outlets and simply recite Bismillah and eat it.
And Allah Ta'ala Knows Best
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