Disclaimer: I am not a lawyer.
The answer to that question is yes. You'll commonly see television or newspaper images of people shopping, or of stocking up before a hurricane.
If the crew has been allowed into the store and videotape a customer, there's really nothing that person can really do. The people photographed can ask the photographer not to use their image, but have no legal recourse. Typically, management of a store has allowed the camera into their store, so the customer only has the manager to complain to.
Now, we are often asked by folks once they see us, "Please don't put me on TV!" I have always made sure their request is honored. There's usually no good reason not to. However, we sometimes do stories about people speeding, and one time a came up to a guy who was speeding and stopped at a stop light (an assistant shot him with our radar gun up the street). He said several times in a tough guy manner, "Don't put me on TV. You'd better not put me on TV."
Well, what's a SURE-FIRE way to get on TV? Bingo... get an attitude. When confronted with a situation like that, I'd suggest two things that would have made that guy look not quite so bad. 1.) Kind of sheepishly say "Sorry. Made a mistake!" People like folks when they admit they're wrong. 2.) Lie or beg. He could have said "Dude, my wife's gonna kill me. Please don't use me!", and I probably wouldn't have used him.
Anyway, back to topic: If there has been a stated or posted prohibition from taking pictures inside a store (a place with public access, but privately owned), and the only way an image could be procured would be by entering the photo-restricted place, then that could be either trespassing (if an individual has been prohibited), or it could possibly be a civil tort. Personally, I would consult my management (who would get an answer from our lawyers) before I would ever proceed like that. Now, if a store (as has happened countless times) has ordered us off the property, then we can shoot anything and everything visible from off-premises and air it, and be in the clear.
Now, if there was no stated or posted prohibition and you took pictures, then were ordered off the property, then we usually run the situation through counsel before running the material. You're in a gray area and must decide whether it's really worth the fight. Sometimes it is, sometimes it's not.
NOTE: I am not a lawyer and anyone can sue for anything on any given day and possibly win given a favorable judge and jury. These are just generally the ground rules understood by most media. 8)