>are we no violating their copyright just by implementing their API?

OpenJDK is GPL. If you comply with GPL, no. This is the problem, Google copied and did not comply with the GPL. Their other option was to pay Oracle/Sun a licensing fee for a commercial license. This is exactly the business model many GPL users follow. Ruling otherwise makes this business model invalid, but it also creates a double standard.

Consider a programming language where you program in types, like Idris. The case is more obvious here. The API is a program. The same applies to Java too, but that seems less obvious. The API is the program that produces compiler output.