I can store anything you give me; that you exposed me to it is consent, it's not your data unless you keep it to yourself. When you walk around a public space, you don't get to control who looks at you and logs it. The products of my labor are mine, and that includes whatever I log in public spaces.
Even in the US which is hardly a bastion of consumer privacy that’s not true. If you as a hotel owner stick cameras in every shower you should expect a set of lawsuits, even though that’s your property and the people have knowingly bought a service from you.
Neither is a store or a website, which were the examples used. But we can translate the same example given to public spaces easily: you install a hidden camera in a grating in a public square and take upskirt shots of women walking over. That’s illegal at a federal level in the US so people absolutely have a legal right to control your ability to do that.
Wrong, a store is a public place, they have cameras, more to the point I can take a photo of you in a store and you can't stop me nor do you own it.
> take upskirt shots of women walking over. That’s illegal at a federal level in the US
Only since 2004, and that's a specific exception that was made and only applies when there is a clear expectation of privacy, i.e. wearing clothes to cover your privates is a clear indication you expect that to be private. That doesn't stop anyone from taking pictures of you you don't like though and it only makes the area under your clothes a private space, it doesn't make the public space your in a private place.