They addressed this post-Crisis by having a snowstorm hit the Kent farm after they discovered Clark. They remained on their farm until spring and emerge to explain Clark was born while they were trapped, and the local doctor certifies the birth.

A broad strokes version of that story is used to explain that Superman is considered native-born because he was still in his birthing matrix when he landed.

Right, that's how Clark Kent would get away with it if the government doesn't know he's Superman. However, Superman is on record admitting he came from another planet (at least in the James Gunn movie), so if the government finds out who he is, Kent could be in trouble