Here's example language from New York City law:

All consumer commodities ... shall have ... a sign at the point of display which indicates the item to which the price refers, provided that this information is plainly visible at the point of display for sale of the items so indicated.

So it is a question of whether the product spilling over to an adjacent shelf still has a "plainly visible" price tag. If it were on a wrong shelf entirely it would not, and here there is some ambiguity, but city inspectors can be pretty strict and demand items stay within the lines. If it is decided the price was not plainly visible, the store may be fined $25-$100 per violation per day. In any case, the customer would not be calling "better business bureau" (which is just yelp from before the internet), but the Commissioner of Department of Consumer and Worker Protection. And the customer would also not get to pay the lower price for the other product if it is clear it is a different product, as the customer admits they knew. (The question would be different if there were ambiguity).

However, the point that I specifically object to is the opinion that it was preposterous for the customer to claim some legal right in this situation, the implication that no such right exists. The language of the law does exist (at least in some jurisdictions), and violations do carry legal penalties.