Honestly, the disclosure probably had nothing to do with the message itself. I'm sure it was all about institutional beliefs and policies regarding plagiarism. If some student took credit for an unattributed ChatGPT essay, they'd probably be pitilessly be given a zero at best.
However, including the disclaimer totally undermined the message (which was a pro-forma thing no one would probably have cared about otherwise). The message said "we care," but the disclaimer said "but not that much," and that would understandably offend people if noticed.