Your question can only be answered by: It depends on the quality of the spinning/re-authoring.
It's garbage in; garbage out...
Whereas if you craft a quality construct, with massive levels of spin (paragraph re-ordering & substition, sentence rewrites and high-quaity spintax) then you'll get your pages indexed all day long. Then, the only factor becomes the quality of the site itself, and not your content. If you're publishing to junk sites, then the content might not stick because of the low 'site value', but this has nothing to do with your content.
I've created multiple networks of hundreds of sites each - using lots of hyper-spun constructs. And every one of them that I still own (and therefore still monitor) ranks and indexes fine.
Spinning is a highly misleading term; as people read different things from it. It can reference auto-spun garbage, built from random snippets at one end of the scale; right up to professionaly written and re-authored site content.
You get back what you put it.
The point about not using spun-content on sites is another side of the same coin. Use bad quality content that looks similar and you risk the look of on-site duplication; which Google hates in any kind of volume (i.e. 500 pages spun-out for geo-coding anchor/ranking-phrase variations etc.) You can do this for your grey/hat-hat 'disposable' assets, but not your prime web-estate. But again, if you're using multiple and varied high-quality constructs, then of course you can use them to build out sites.
And remember spinning/re-authoring applies to all content; not just the body content. So titles and bio's and links/anchors etc. - anything that can leave a footprint. And this can apply to layout/structure as well.