It’s a misunderstanding (possibly deliberate) of UCC § 3-311’s accord and satisfaction provisions.
In particular UCC § 3-311(a)(ii) requires that the amount due be a matter of bona fide dispute (i.e., “the store sent me a bill for the full price, but I contend I had a raincheck that entitled me to a sale price.” NOT “the store sent me a bill, but I decided, after buying on credit, that I didn’t want to pay as much as we had agreed, so I sent them a check for 20% of the bill and wrote ‘PAID IN FULL’ on it”).
Moreover UCC § 3-311(c), imposes, in addition to the substantive requirement of a bona fide dispute as to the amount owed, procedural obligations on the obligor whose obligee is an “organization” (like a bank, or credit card company, or utility company). In that case, if:
(1) within a reasonable time before the tender [of the “PAID IN FULL” check], the [business] sent a conspicuous statement to the [billed party] that communications concerning disputed debts, including an instrument tendered as full satisfaction of a debt, are to be sent to a designated person, office, or place, and
(2) the billed party doesn’t send it to that designated person, office, or place
then there is no discharge of the obligation, the annotation “PAID IN FULL” notwithstanding.
(To be completely comprehensive, if there is a bona fide dispute and the recipient is genuinely notified that the check is being offered for accord and satisfaction and the recipient takes payment on the check, the obligation will be discharged.)
The provisions of paragraph (c) were meant to allow automatic processing of checks without throwing an accord-and-satisfaction monkey wrench into the mix. Generally, major businesses will be able to avail themselves of 3-311(c) because there communications will have contained notices about where to take disputes and it will not be the general remittance address. The workers at this special disputes address will obviously be on the lookout for checks that attempt to assert accord and satisfaction and will return them to the customer uncashed.