I have no idea about U.S. Laws, but here in England, I believe, the lower price is the legally binding price. Where I work, the shelf ticket can be higher than the barcode price - which is what the customer pays. If however, the shelf ticket price is lower then the barcode price, and the customer spots it, we charge the lower price. I believe this is a legal requirement.
Obviously, we have teams of people working to check that all tickets and barcodes match.
Mistakes are made, but the customer should get any benefits of our mistakes.
Here in the UK, retailers do not have to sell anything to anyone, just as technically, I believe the customer should pay with correct money and cash change isn't legally required (but retailers wouldn't last long if they didn't give change!)
I'm not well informed on these issues and I'm happy to learn more and be corrected.
Al