Even the taint on saidin doesn't strictly demand divine interference. The fate of Shadar Logoth demonstrates that man-made supernatural corruption can also occur, and the events of the ninth book even indicate that gur zntavghqr bs gur gnvag ba Funqne Ybtbgu vf rdhny gb gur gnvag ba fnvqva, fvapr gurl obgu ryvzvangr rnpu bgure. So it's not vanishingly unlikely that humans could have tainted saidin themselves. The Blight and the Darkspawn are physical corroboration of the narrative that involves conflict with the Dark One though, as is the taint on saidin.

If anyone who's not a Darkspawn or one of the Forsaken has actually been to Shayol Ghul and made it back to tell about it, that would provide additional evidence, but as far as I can tell the only reason anyone on the light side knows it exists is because the legends say so, and maybe because trollocs and myrdraal have attested to it on some of the rare occasions when people actually talk to them.