So, this is a slightly different mantra. Working backwards from the customer is an important thing. And if you know that customers will be using your product programmatically, then yes, building the API first is important.

But note, in that world, you aren't necessarily building tests of your software. You are building specifications for your API. I can see how these might be seen as similar. And for large portions of your code, they can be.

However, for the vast majority of your code, it exists to help out other parts of your code. Not to be used as a library/framework by others.