Is the cowbird native to Earth or a species brought here by extraterrestrial interlopers?

This is an extraterrestrial species. The behavior and characteristic are the giveaway. You can see this in other predatory species. Those are typically interlopers. There is always an element of competition in nature because there must be sharing and sufficient resources to serve all. When such is the case there is harmony and animals can feed side-by-side with no tension. When resources are scarce there will be a competition because all organisms have within, the drive to succeed and to preserve their life. This is the nature of the instinctive desires of thirst and hunger that can become quite compelling and override almost anything, including moral qualms about taking something from another, even on the part of high-level intelligent beings like humans. Humans are a poor example, and a poor standard almost always, in comparing to nature because they are so corrupted by the interlopers. But when food is available, all can live in harmony and peace and there is no natural proper place for a species that only survives by preying on another. And so, this is the characteristic setting it apart from what would otherwise be a natural order for Gaia. This includes the hawk as well, and the shrike. The latter, in particular, is noteworthy because it kills for the sake of killing. This is very much akin to the other predatory species you know already are implanted here to be a source of corruption and a downgrade. Some are more for the sake of leaving a calling card, but most are deadly serious, especially those that worsen humans directly, like disease-bearing species that suck blood or cause a parasitic infestation.