Unless you actually saw it being squeezed, I wouldn't consider it "freshly squeezed". This is also the first time I've seen anybody, outside of advertisement, describe Minute Maid as "premium" orange juice.
Over here some supermarkets have juicers pre-filled with oranges in their produce sections, you just put an empty bottle into it, push a button and you can watch live as it squeezes the oranges into your bottle.
Don't know if they exist in the US, but I specifically look for juice bottles that say "NOT FROM CONCENTRATE". I can usually find a few even in smaller grocery stores.
