I've never heard this. I'd say each dealer has their own policy.
I have not heard that before and I used to sell automobiles.
That, most likely, is not a Chevrolet thing. Depending on individual dealership/repair/service shop policy, they may not deal with the repair of an older model but I'm pretty sure they should do maintenance service. (This is not a certainty just an educated guess.)
Thanks! Your answer is awaiting moderation.