They don't need to avoid the perception of bias because they're free to run their marketplace however they want. They have absolutely no obligation to look out for anybody's interest except for their own.
But, FWIW, it totally makes sense for them to have different rules when the third party merchant fulfills orders. Amazon and merchants selling on their platform have different incentives. Amazon cares a lot about their customer experience and has an extremely long-term perspective on customer satisfaction. Many third party sellers are either 1) incompetent, or 2) actively malicious. As a result, Amazon has to structure incentives accordingly whenever they let a third party seller handle part of the customer interaction.