You, and your source at Apple, are quite clearly mistaken about these claims.
There is no law, statute or other legal requirement that the case and LCD of an iPod, iPhone or similar product be replaced before it is sold as refurbished. To claim that as so is simply ridiculous. Decisions about how to handle the reconditioning of items intended for resale are guided by internal rules at Apple and those promulgated to their contractors.
Refurbished Apple products, now termed 'Apple Certified Refurbished' products—but, long popularly known as 'factory refurbished' Apple products—originate primarily from dealer and distributor returns, are the result of product discontinuations, or come out of Apple's service, recycling or similar programs. Before they are sold as Apple Certified Refurbished products, they are repaired or reconditioned as required, repackaged and generally sold primarily through the many online Apple Stores, including those reserved for education or business customers, or specialty stores created for the exclusive use of specific organizations, colleges, community colleges or schools. Most, though not all, refurbished products are repaired, reconditioned or repackaged by Apple contractors such as Flextronics.
Such repackaged products generally retain the 11 character serial number of the original product (though that was not always the case) and usually are categorized by a newly assigned marketing number beginning with the character F. An 8 gigabyte iPhone, for example, originally marketed using the MA712LL/A marketing number is re-designated an FA712LL/A product when repackaged for resale as a refurbished item.
Some authorized dealers, particularly those badged as Apple Specialists, can and do sell refurbished Apple gear which they purchase in bulk, directly from one of several Apple program sources. Refurbished products carry a one-year Apple warranty, and are eligible for extended AppleCare coverage.
Because Apple has so many program sources—internal ones like the AppleStore for Resellers, and the several take-back programs involving Apple Finance and the recycling programs Apple now administers, and external relationships with distributors such as Bell, Ingram Micro and Tech Data, its own company-owned Apple Stores, its online resale outlets and its dealer, dealer affiliate and service providers, it is difficult to apply a universal description of the process of handling Apple Certified Refurbished products. What I outlined above is likely the closest and most accurate description that can be applied to these many related programs.