I just found out that Amazon's API no longer returns any customer reviews, but instead it provides an URL to a page on Amazon which contains the reviews, to use the URL in an iframe. The URL contains SubscriptionId.

I've checked a few of the review pages that Amazon returns, none of the on-page links contain any affiliate tracking codes. The pages themselves are regular Amazon review pages, not custom review-only pages.

Now, I'm not sure which cookies are given due to clicking through an affiliate link, so I can't confirm that having an iframe with SubscriptionId in its source URL causes cookie stuffing.