The things people say aren't truly independent, even when they are. Like when Charles Sheffield and Arthur C. Clarke wrote novels with the same plots at the same time, they were working independently, but they weren't culturally independent.
Besides, even if several people independently assert "tying a ribbon to a wishing tree cured my warts", that's not an explanation of what actually took place. If repeated observations with unbiased instruments confirm this, then there's something wrong with the instruments (or something), until you have an explanation.
(But saying things like that usually prompts people to bring up cosmology or particle physics or other fields where we really do have to resort to saying "the measurements say it's happening, we'll have to assume it's happening" without understanding much.)
Besides, even if several people independently assert "tying a ribbon to a wishing tree cured my warts", that's not an explanation of what actually took place. If repeated observations with unbiased instruments confirm this, then there's something wrong with the instruments (or something), until you have an explanation.
(But saying things like that usually prompts people to bring up cosmology or particle physics or other fields where we really do have to resort to saying "the measurements say it's happening, we'll have to assume it's happening" without understanding much.)