I very much doubt there's a significant downside to class 3 inspection when you specified class 2. After all, class 3 is for critical equipment so your boards were inspected to tighter tolerances, etc. I obviously was not a party to your conversation with the manufacturer but I think that what you are interpreting as "caginess" is really just them not seeing it as a problem that requires much extra thought or explanation.
As for your points: a lot of the class 2 vs class 3 differences are pretty straightforward "50% overhang vs 25% overhang" type tolerances and it's entirely possible that they inspect to class 3 automatically since that also satisfies class 2 criteria without having to worry about mixing up two sets of criteria. Also some of the class 2 criteria - while more permissive - are trickier to inspect. As a (made up) example: class 3 might specify 100% solder coverage on a terminal but class 2 might allow 75% coverage on a vertical portion if the terminal height is 1mm or less and 50% coverage if the terminal height is more than 1mm but then also requires horizontal coverage of more than 75%, etc.
Increased costs due to scrapping defective boards could be there, but they didn't get passed along to you and I think you'd be as likely to see rework costs. And unless you're going by some really fly-by-night place I doubt they're scrapping a bunch.
Increased solder cost: unlikely, unless you've specified some exotic solder. The standard itself doesn't really translate into class 3 = more solder. In fact, excessive solder that obscures inspection of a joint could be a failure condition.