Dash
that isnt much of a question A hashgacha on an establishment doesnt mean that they oversee the kashrus of every thing inside, rather that they trust those who do. If say the Star K gives a hechsher on a pizza store the tomato sauce might be under the chaf K, the cheese under the hisachdus, the flour under the OU etc etc.
Similarly bottled drinks are either under their own hashgacha which the oversseing hashgacha recognises or the overseeing hashgacha feels that they don’t need one (eg water)