Legitimately Altered Check?

A customer presented a personal check for deposit from an account that they own at another financial institution ("New Bank"). The"New Bank" bought another bank ("Old Bank") about four years ago. This customer appears to have retained their check stock from the "Old Bank", but they have made paper copies of the "New Bank's" logo, as well as the MICR line containing the "New Bank's" routing and transit number, and the customer's "New" account number. The customer has carefully cut out the paper copy of "New Bank's" information, and glued it on to their "Old Bank" check stock, aligning the logo and MICR information, as they would have naturally appeared on properly printed check stock. The alteration is more than obvious (imagine: white copy paper glued onto a "fashion check" with the image of a moose wading in a creek). We were able to verify that the customer does own the account at "New Bank", and the customer is in good standing with both our institution and the "New Bank". On our end, the Check 21 check image is acceptable despite the glaring alteration, so the check will be processed and paid without incident. (We know this because our tellers have apparently accepted these in the past without pause). It really appears that this customer is just being extremely frugal or environmentally friendly in wanting to use her check stock from the "Old Bank". Is this right? Is it true that a negotiable instrument could be written on almost anything? Is it simply up to the willingness of the financial institution to accept it?