It's called a "public accommodation", and it is indeed open to the GENERAL public during business hours, unless the place is rented out. You are conflating "public" as in publicly-owned (such as sidewalks that aren't actually owned by private individuals) with "public" as in public accommodation such as privately-owned restaurants. There is not an expectation of privacy in any general area except bathrooms and marked rooms. If there was, you could be sued (or even jailed) for taking a selfie in a restaurant and picking up anyone else in the background. If you had an expectation of privacy, security cameras would be illegal (like they are in bathrooms and hotel rooms, where there's an actual expectation).
You're simply out of your mind if you think there's a general expectation of privacy in any public accommodation. There are exceptions, e.g., privately-owned places open to the public can be marked as photography-free zones, such as museums and art galleries. Public places can have private events with their own rules, including renting out a public park. Entry may come with a contract, such as sports tickets and concerts. Some public places may prohibit all recording, such as SCOTUS.
As far as photography goes, entering the general areas of a public accommodation is the same as walking down the sidewalk. The only difference is that the owner can throw you out, as long as it's not based on your race or something. A restaurant is in public, you can be recorded, and you have no "right" or expectation of privacy or "right" to the recording. The photographer, in contrast, has a "right" to record you in public (with some limitations... some states prevent surreptitious recording and some have tried to prevent sound recording, recording of boondoggle animal-cruel farms even from public places, etc, and of course if you're told by the property owner not to record, you can't -- that's what TFA is whining about, because he got thrown out for carrying a recording device.) If you have to have privacy when you dine, then you have to dine in a private room or house where others are not allowed to enter, with the curtains drawn. Or, you can dine in a bathroom or locker room. Yum.
Privacy is not the reason photojournalists cannot enter these public accommodations. It's because the business owner won't let them harass their guests, since it's bad for business. If a photographer enters or lingers after being (legitimately) denied entry, they are trespassing, and can be hauled off.