Again this is one side of the argument. Remember that the fasting body is far more conservative than the consuming body. So the nutrients that are usually lost through sweating are very likely reduced or even stopped altogether and only toxins are released. I read one account of a faster who stated that he even stopped sweating salt while fasting, and that sweat that dripped into his eyes did not sting them.
Basically the two options are there, there are pro's and con's for both. So it's best to make up your own mind. Or experiment for yourself being careful not to overdo it.