Amazon's automated system has a warning that auto-appears unless you select: "Don't show this again." as shown below:
Amazon's public facing statement is not a new position as they have always recommended that you rent your codes from GS1 (GS1 is a private organization, not a government org. Also amazon later joined the board of directors of GS1 in 2016).
Amazon being a private, unregulated company can say and act however they wish, but this statement alone does not keep you from being able to use your legal GTIN's, this is due to GS1-USA's class action suit & settlement as detailed here: https://www.barcodestalk.com/ucc-settlement They are trying their best to keep legal owners from using their codes and resorting to this type of fear tactic.
At this time there is not an actual mechanism in place on amazon's general platform that would or could enforce what they are stating. However amazon can manually and individually choose to discriminate against your account if they desire, regardless of your legal ownership of GTIN's.
If this topic is new to you or your business please read the differences in renting from GS1 & owning from Bar Codes Talk here: https://support.barcodestalk.com/en/support/solutions/articles/16000020109-will-my-bar-code-work-with-amazon-ebay-google-