Actually in most of these threads (I've read through a lot of them trying to diagnose my own issues) the google product experts say not to use the disavow tool, lest you accidentally disavow links that may have been helping you. (ie. presumably google is smart enough to ignore those links)

This runs counter to my anecdotal experience, which is that disavowing spam links has an almost immediate effect, if the rank fluctuation is caused by those links.

The "disown" bit is interesting. I do wonder about their ability to discern "oops" versus "someone is targeting me". And the idea that negative SEO is even happening in the first place.