That claim is probably true, but the manufacturers warranty only covers the original purchaser. Warranties are seldom transferable and not at all without the manufacturers permission. Clear case of a seller trying to sell something he is not authorized to sell. You can't sell an equipment warranty to a third party without first party authorization. The original warranty grantor has no way of knowing the condition of the used equipment being offered for sale.
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Warranties are overrated anyway. The fine print lists the exclusions that make the warranty limited. Warranty coverage is usually limited to cover problems that are very unlikely to occur. Sort of like insurance. They insure against loss and then force the insured to eliminate all possible risks that could result in loss.