Generally, its anecdotal evidence...
I always advise clients against them because of many cases where they 'could' have been the culprit. Generally though, there are always other factors, and I've never actually seen any conclusive evidence that they damage an SEO ranking in isolation.
Typically, I've seen cases where WordPress sites have used some plugin, either on-purpose for SEO - or unknowingly, and created 10k+ links across an entire site. The site that is linked to has experienced problems, but this could be for a variety of reasons. Maybe it has increased the density of a single keyword, or maybe that many links from one site has tripped another filter (nothing to do with this) which has then caused another negative effect to trigger, or even a manual review in some cases. (Domino effect.)
Google should of course be 'clever' enough to just discount a massive amount of links from a single domain, especially in light of the amount of WP plugins etc. that can cause this. So, I'm in 2 minds with it. But since it has appeared as one of the obvious possible contributing factors to a large number of negative ranking cases I've looked into, I've always avoided it as a matter of 'just-in-case', largely because there is very little ranking benefit to be had from 10k links from a single domain as compared to 1-10 in embedded content. I believe that multiple links from a domain can be useful over time and when appearing naturally, but obviously not hundred or thousands.