This is baseless as there is nothing to support such a claim. No problem in
throwing them away.
What is referred to here by “menstrual rags” is the rags which were used for menstrual blood, as al-Mubaarakfoori said in his commentary on this hadeeth. So it seems that they used to throw them away when they were contaminated with blood, otherwise the Sahaabah would not have raised the issue of whether the water into which these rags were thrown was taahir (pure) or not.
There is no sound basis for what your friends have said; rather it is a myth which has no basis. Such notions are widespread among the common folk, so you have to ask for proof and evidence, and refer to the scholars and books of knowledge. You have to reject these myths and warn people against them. Each person must protect himself against the evils of the devils among mankind and the jinn by remembering Allaah a great deal (dhikr), reciting Qur’aan and adhering steadfastly to the commands of sharee’ah, and keeping away from myths and stories that have no proof. And Allaah knows best.