We may be arguing semantics, whether it's a dog being "mad" or "anxious" or "spiteful" the results are the same. House soiling is a frequent result of separation anxiety.
Since this behavior happens only when being left alone, it seems apparent to me that it's not a house training issue. If you change how the dog reacts to the initiating stressor, the behavior will change. The article I referenced above has some methods on how to approach this problem. Easy to say, not always so easy to accomplish.
That's where the feeding, exercise and environment changes would be useful in eliminating the symptoms. If you need to, contact a behaviorist or your vet for specific treatment recommendations and/or medications and supplements that could be useful.