It most absolutely does apply to maintenance. Sure, lots of lawyer speak in this...But if the manufacturer requires use of a specific part/product/brand for the duration of the warranty, then they must provide that product for free. It includes all maintenance which must be performed on the product.
From the definition section:
(9) The term “reasonable and necessary maintenance” consists of those operations (A) which the consumer reasonably can be expected to perform or have performed and (B) which are necessary to keep any consumer product performing its intended function and operating at a reasonable level of performance.
From section 2302
(c) Prohibition on conditions for written or implied warranty; waiver by Commission
No warrantor of a consumer product may condition his written or implied warranty of such product on the consumer's using, in connection with such product, any article or service (other than article or service provided without charge under the terms of the warranty) which is identified by brand, trade, or corporate name; except that the prohibition of this subsection may be waived by the Commission if—
(1) the warrantor satisfies the Commission that the warranted product will function properly only if the article or service so identified is used in connection with the warranted product, and
(2) the Commission finds that such a waiver is in the public interest.
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