You're 100% right. What we're describing sounds a lot like waterfall. Here are a couple more details:
* Our team of devs have collectively built over 450 websites. We know the domain well.
* We also did a lot of UI design early on that guided some some of our work.
That said, we didn't just design and give birth to a great API. We have iterated on a it a lot. Our clients were going on HiFi 6 months prior to the public release. We learned a lot and iterated on the API quite a bit during that period.
What ended up being nice was the ability to make sweeping changes at one point (the API) that benefited the entire application. This is a huge advantage.