It's hard to say about the chain. A chain can be worn even though it doesn't show up as stretch, so that alone doesn't mean anything. Also, bikes definitely shift differently with a new vs used or worn chain, (even chain lube can make a difference) so they might have a point vis a vis the chain. That's might, so giving them the benefit of the doubt, it's a borderline pass on the chain.

However the tire sheds another light on the whole deal. There's almost no reason to [edit] automatically replace a tire that isn't either worn through in places, or has a damaged body evidenced by bulges or twists. Making you buy a tire for a tuneup isn't appropriate. Maybe a warning that the tire's near the end and you shouldn't leave town with it, but that's as far as I'd let someone go, either as a store owner or customer.