Is the presence of water on the lower back when passing gas, believing it to be perspiration from the rear and not something that invalidates wudu, considered a way to ward off obsessive doubts (waswasa) or a form of leniency, especially upon waking, or feeling the urge to relieve oneself, or in cold weather?

If a person finds moisture and doubts whether it is sweat or something that exited from the anus, the default assumption is that nothing exited from the anus. Therefore, it is not considered a nullifier of purity merely based on doubt. Adhering to this principle is particularly important for those afflicted with obsessive whispers (waswasah); they must disregard such thoughts and not rule that something has exited except with absolute certainty.