This always struck me as a blatantly disingenuous generalization.
What are the two services being described here? It matters very much.
If my product is an email platform, and the "API service" accepted the "send email" request by enqueuing a "send email" message for the "email sender service", if the "email sender service" is down, it absolutely does degrade the experience of API service users: "your email is sent" vs "your email will be sent as soon as we're able" is two very different promises.
I think I'd like to work for the company who doesn't care about the difference in those two promises. It'd be very easy to just implement the worst possible solution and provide the flakiest possible experience. Of course, I haven't seemed to find those employers yet in my career. Everyone wants reliability and performance and everything else that sounds nice, all without specifying how the product should really behave. Where are the companies where I can implement these brilliant solutions without the downsides?