In order to convert oils to soap, a very strong base -- like lye, sodium hydroxide, NaOH -- is needed to alter the fat or oil molecules.
There are no such strong bases in the human digestive tract.
Even so, let's pretend for a moment that there were.
The saponification process is very exothermic. In other words, if the body were creating quantities of soap from the half cup or more of oil you drank the night before, it would also be cooking your insides. Ouch.
Then consider: why would olive oil and apple juice result in these stones when all the other fats and acidic liquids you've consumed in your lifetime never did? Surely, if the body were saponifying olive oil, it would be saponifying all the grease and fats we eat -- everything from fresh vegan guacamole all the way to greasy fast food french fries. All these fats would also be being "saponified".
The body can't use saponified oils.
Further, if you want to test soapiness of a substance, see if you can make suds with it. Even early in the saponification process, even with botched batches of soap -- too much lye, not enough lye, wrong temperatures, whatever -- the resultant glob is still sudsy. The stuff you found in your stones... doesn't make bubbles, does it? So no matter how much you might think it's "like" glycerin soap, it isn't glycerin soap.
And if the digestive system were in fact routinely saponifying oils, then all your excrement should have a sudsy character to it. I don't know about yours, but I have never found suds in the toilet after defecating -- not even from explosive diarrhea -- nor in my children's diapers, nor in public toilets when someone opted not to flush.
So could we please put the soap hypothesis to rest?