"It's not a huge surprise that some sites which went way too far spamming for links will sometimes go overboard when it's necessary to clean the spammy links up. The main thing I'd recommend for a site owner who gets a fairly large number of link removal requests is to ask "Do these requests indicate a larger issue with my site?" For example, if you run a forum and it's trivially easy for blackhat SEOs to register for your forum and drop a link on the user profile page, then that's a loophole that you probably want to close. But if the links actually look organic to you or you're confident that your site is high-quality or doesn't have those sorts of loopholes, you can safely ignore these requests unless you're feeling helpful."
Yes, we work to avoid this sort of attack when designing our ranking algorithms.
The most likely situation is that the company who sent the letter hired a shady SEO. That SEO did spammy things that got them penalized. They brought in a new SEO to clean up the mess, and that SEO is trying to undo all the damage the previous one caused. They are trying to remove every link they can find since they didn't do the spamming in the first place and don't know which are causing the problem.