Is it true that moldy jam/pickles are good to eat if you mix the mold into the rest of the mixture? Everyone in my family says that when you see white mold on jam or pickled goods, you shouldn't bother with throwing away or removing the mold. All you have to do is to mix it back into the rest of what's in the pot. Here is an example:

I would like to know if it's a myth, because I feel something evolutionary in me that tells me simply mixing it back into the water is a bad idea.
Unless there is good reason to assume it is not mold/bacterial colonization, but some other precipitate as explained in other answers:

There is no scientific reason at all to assume that such a method is safe, certainly not for any random pickle made by any random recipe spoiled by any random white mold found in any random environment. While some very acidic pickling liquids might kill the mold or bacteria, it will not deactivate existing aflatoxins or bacterial toxins.