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Keep in mind that there are two parts to the federal judiciary in the US: the Supreme Court, which is independent, and the lower courts, which Congress establishes by law.
Because the Supreme Court is independent of the Legislative Branch, it has other processes for setting its rules. THAT's what Thomas was referring to.
The judicial branch employees referred to here are just those that Congress has jurisdiction over.
Not to mention, Thomas would probably argue that those who gave him gifts did not fall under either of the two requirements you included.
