OK, let me clarify.

Let's say a software vendor out there is making a ton of money with a product that exposes a certain API.

Let's say I know a way to implement that API in such a manner that its performance will be improved by an order of magnitude. (without using any patented method in my implementation)

Can I put together that implementation and market it as a competitive product?

In my experience, APIs of commercial products are disclosed under the terms of their licensing agreement. So, one could argue that I cannot market a competitive implementation, if the license terms I agreed to (to gain knowledge of the API itself) prevent me to do so.