BBB accreditation is a big deal for most major companies, and it includes an obligation to resolve issues (exactly like this one) with their arbitration. I've used them 3 times, with 3 positive (and rapid) outcomes.

Next time you have a straightforward 'they're wrong' issue with a company where you're getting outsourced flowcharts for support, try out the bbb. They're great.

Small claims would obviously also work, but that's a major investment in time/bureaucrazy, while a bbb complaint can be completed online in 10 minutes with maybe one or two brief follow-ups, but usually all it is, is them getting in contact with a human who can do things - and for cases like this, they obviously try to make it right.