Apparently it's against Amazon's API terms to compare with other sites. I recall years ago the guy who runs the site explained that he is only ok to compare Amazon with Amazon.
I don't think it's against the rules, but the rules are complex and spread all over multiple places, and they're like Google in that you have no due process if someone there decides they don't like what you're doing.
It is against the rules. If you are an e-commerce company (i.e. a competitor) or you operate a shopping comparison service, you are not allowed to use the API at all.
That appears to be specific to their advertising API, not the affiliate program. The affiliate program policies[0] say:
> if you choose to display prices for any Product on your Site in any “comparison” format (including through the use of any price-comparison tool or engine) together with prices for the same or similar products offered through any web site or other means other than an Amazon Site, you must display both the lowest “new” price and, if we provide it to you, the lowest “used” price at which the Product is available on the Amazon Site.
... which implies that it's not forbidden, but I can't blame someone for not wanting to risk it.