This misrepresents the situation. Authors accepted manuscripts (AAM) have been shared on institutional and subject repositories for around two decades, with greater prevalence in the last decade. Despite this the version of record (VoR) is still valued and preserves the integrity of the scholarly record. The integrity of the VoR continues to be maintained by the publisher and where well-run repository management are made aware, corrections can be reflected in a repository. The solution to this problem is the publisher taking their responsibility to preserving the integrity of the scholarly record seriously and notifying repositories, not asserting that authors should not exercise their right to apply a prior license to their AAM.

So far as I know this is not tested or based on any evidence. If the publishers think an open accepted manuscript would undermine the version of record, it doesn't demonstrate much confidence in their added value to me.