No evidence of this whatsoever. A bluecheck on Twitter loudly proclaiming that he's not going to pay $99/yr for email (HEY) or never using Basecamp again doesn't count. Citation needed.
Most might be broad. Lots of companies absolutely care about the interal workings of their vendors. They can and do make decisions on these kinds of factors, especially if a large contract is on the line or they are looking for that last thing to separate 2 viable candidates. All companies doing manufacturing in places like Asia are constantly being looked at by human rights organizations to ensure the employees are being treated as humans. Personally, I won't do business with companies like Uber (even with new leadership), Wal-Mart, etc based on things reported about them.
I doubt that, most companies could not care less about the internal affairs of their tools' companies, unless it impacts the tools' performance and featureset, something we still await to see regarding Basecamp, whether they can successfully plug the employee hemorrhage wound and get new employees working on the product.