* No website or app should ever call out to any third party API
* Every single piece of functionality a website or app has should be developed in-house
* The functionality third party APIs provide would often take "a few days" to reproduce in-house
Definitely. Your website and app should only call your APIs. Your API can then call the third party API from the server. It's a lot easier to change something on the server than having to update the app.
It's not really addressing the whole issue of depending on third party APIs if your API is calling on them, but you are technically correct, which I've heard is the best kind of correct.