I've felt from the first time I ever heard of ROS (run of site) links that they couldn't possibly be natural. This view changed slightly with blog rolls, but only if they represented a small chunk of a site's inbound link profile. Scaling down from ROS links to c200 inlinks, it's unlikely that that many links would occur naturally either. Perhaps if you're Microsoft, it's natural that you'd have 200 inbounds or more from Wikipedia, but in general, a number that large will probably raise a flag.
IMO, that flag will be weighed against other signals Google has about your site. In your case, it sounds like you didn't artificially build backlinks, so I wouldn't lose sleep over the situation, but, depending on other factors I'll mention, I'd do my best to get rid of the links.
Try a nice email request first. Perhaps, if these sites later try to extort money from you, you could suggest to them that they leave you no choice but to use the Google Disavow Tool, which you understand might adversely affect their reputation, and you wouldn't want that to happen... etc.
I suppose this kind of situation could devolve into Double Negative SEO, a whole new thing to look forward to. ;)
There's one view that has it that you should consider ongoing pruning of obviously manipulative links as a part of site maintenance. Those who promote that view suggest that the backlink quality bar is likely to rise over time. On the other hand, disavowing links can be an incredible waste of time and energy, better spent on creating good content, and I can understand those not wanting to do it.
It very much depends, I suppose, on how strong your current link profile is, and on the quality of your site to attract good inbounds naturally.
If your backlinks are weak and you think you might be vulnerable, getting ahead of the curve and pruning the worst of your backlinks might not be a bad idea. If you do this, keep notes in condensed form in a spreadsheet, noting email requests sent, dates, etc, to include in future Disavowal requests... just in case all that becomes necessary.
