The cig lighter part of that charger won’t work on many cars as the cig lighter is disconnected when the key is turned off. You would have to hard wire it in on many cars.
Machinery? There’s no special equipment needed to test a Honda battery (or any particular maker’s battery, that I’ve ever heard of). They didn’t have enough intelligence, maybe - or they were caught trying to sell something not needed and that’s the lie they thought of to get out of it.
Dealership service is (usually) fine, but that doesn’t mean all non-dealer service is crap. Mass marketers that tend to advertise on price (e.g. Sears) usually don’t have top-grade help and often focus on selling, selling, and selling. But there are plenty of good quality independent shops with competence and intergrity, and there are reasons that many satisfied, non-ripped-off customers choose them over both chain operations and dealerships.