No, that is incorrect. The BSD case was about loss of copyright through
failure to include the required copyright notices (a requirement that has
since been abolished). The discussion about the header files applied only
to the trade secret aspect of the case. There are several cases in this
area and none of them is very good. However, on general principles it
should be the case that you can use those portions of an API that are
essential to access and use public interfaces of a library or object. The
problem is, most APIs include far more than such essential interfaces.