It's a little ridiculous to assert that no one should rely on proprietary software. Are all the folks writing Windows applications or PlayStation games idiots? A cautious approach toward relying on an API that's not central to another company's business is the key.
As a counter-point, the Facebook APIs are pretty crucial to Facebook's business (third party developers and application functionality for users), but they've seen plenty of instability and breaking changes in the past, many of which cause real problems for businesses.
If you're aiming for the user-facing side of your business to be self-reliant, under your own governance, and at the mercy of your market rather than of your partners, then it can and does make sense to look at self-hosting open source services and components; you pay a premium for the hosting, but you know that you opt-in to upstream changes on your own timescale, and you can fix issues yourself.
In reality it is indeed tricky to be so disciplined, and if some suppliers provide very high-uptime services with reasonable failure modes (e.g. Google Analytics), then it seems fair to go that route - but on the flip-side, data really is money nowadays, and user privacy may be important if you care about such things, so even these decisions can be questionable.
