The comment about carrots opened a memory of my dad. 
We had a brooder house that we towed away and the dirt under it was very black but also it had been churned up by gophers or rats.  Dad raked the dirt level and planted potatoes in it.  It's unlikely that the hardwood floor of the brooder house ever leaked much manure into the ground, especially since I don't recall it ever having chicks in it for very long at a given time.  Most of the time it set empty.

The year that dad grew potatoes we had easy digging to get them out of the ground.  However many of them were the size of a loaf of bread.   I've never seen such huge potatoes before or since.   I can't help but wonder if it was a combination of soil that had no pathogens and soil that was very loose.

We live in eastern Iowa, not Idaho.   Like the lady from New York City said when told "we're from Iowa", she said, "we pronounce it Ohio, here."