I'd happily hang out their dirty laundry on Meta Stack Overflow (e.g. not withhold the company name) to make users aware that someone is trying to astroturf their product. That way the community can look out for the activity and nip it in the bud. And it should act as a deterrent against any other company thinking to buy exposure like this.
Don't worry about 'copyright infringement' claims on the email. A redacted and summarised email is already no longer a full-on copy of the original and fair use should apply there.
And don't worry about 'any PR' being 'good PR' here. Someone else posted the same email to Meta.SO with the company name intact, and as a result the community has cleared out all remaining references to the product name and is in the process replacing all links to company pages. Clearly, this action is resulting in no mentions of the company at all.
In fact, that Meta.SO page is now a top Google hit for the company name, listed right below the company homepage and social media pages. Great PR, having the first hit for your name outside pages you control be an expose on how you tried to buy your way to astroturfed PR.
If you feel that by sticking your neck out you'll end up getting nastigrams from said company, at the very least forward the email to the Stack Exchange team. The team can then handle it from there. Spamming-by-proxy is still spamming and the team appreciates getting a heads-up on potential problems ahead of time. Also see Tim Post's response on Meta.SO.
