A layman's way of putting what though? Is what I'm asking you. "Sloppy" implies that the effect is undesirable...?
Compression is a standard process, but over-compressing to the point of causing distortion is difficult to do by accident. The vocal is quite compressed but not that much. Regular compression does tend to make existing distortion more apparent though, and applying a distortion effect to something post-compression tends to makes the distortion more consistent, since most distortion effects are amplitude-dependent.
In terms of it not making sense as a post-production effect, how do you figure? If it's not just the highest (amplitude?) notes, then it can't be clipping in the analogue signal path - since that would obviously be focused on transient peaks. Normal harmonic distortion from a valve preamp still fits what I'm hearing, as would a post-production effect designed to sound like harmonic distortion from a valve preamp. Even if I'm not hearing whatever it is you're hearing, I can't really think of any other sources of analogue distortion that would make sense. In my experience, accidental distortion is rarely so subtle.