Copyright (in the US) was literally created by the same people who wrote the 1st Amendment. Copyright is in the Constitution itself. It was very obviously an exception from the start.

"Foreign governments saying things" also existed at the same time the 1st Amendment was written, and there were no carveouts from 1st Amendment in light of that.

In any case: If SCOTUS during its early cases on copyright law (or copyright on the Internet) simply asserted "this has nothing to do with the 1st Amendment," they'd also be wrong. That would be a clear avoidance tactic not to wrangle with the substantive issue. In reality, the big cases on copyright are riddled with 1st Amendment questions, considerations, and constraints.