All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
As far as we know, the supplication of "As-Salaamah" is not legislated in Islam. Furthermore, starting the supplication by reciting Al-Faatihah (the opening Chapter of the Quran) collectively (in one voice) has no basis in religion as well. There is no doubt that specifying a given supplication and naming it “the Supplication of As-Salaamah” is an innovation in religion, as the Prophet said: "Whoever introduces into this matter of ours [Islam] that which is not a part of it, it will be rejected." [Al-Bukhari and Muslim].
If the group of people whom you mentioned did not intend to specify a given supplication and do not believe that it is permissible to recite Al-Faatihah at its beginning, then they should in any case avoid such acts, because many innovations start at the beginning in this manner, and then the people adopt it and believe that such an act is permissible. Consequently this act becomes (in the minds of people) a recommended Sunnah. The one who first innovated such an act will be the one who bears its sin and bears the sins of all the people who follow him in doing it, but those who do it are also sinful for their act (for doing this innovation).