Well, Science & Nature certainly don't exclusively publish neuroscience, but either way it was a gross exaggeration (which was kind of the point). Very few psychologists, neuroscientists, or anyone for that matter is likely to publish there at any point in their career, let alone as a grad student. They are just my "Go to" prestigious journals as they publish stuff in my area so they are first ones that come to mind, are widely known, and carry weight across pretty much all fields. Feel free to insert any other journal of your choosing with an IF > 20🙂 Not that IF is the end all, be all...
More realistically for most of us, a publication in Psych Science, JPSP, Abnormal or JCCP will almost certainly open doors. Not that they are really in the same league as Science/Nature in terms of prestige, but within psychology specifically they are top of the line, though I'm still not certain I'd expect one first-author pub in one to guarantee one would be competitive at research-heavy internships.