> If you added a simple additional to the problem, such as "Note that in this context, 'if' only means that...", most people would almost certainly answer it correctly.

Agreed. More broadly, classical logic isn't the only logic out there. Many logics will differ on the meaning of implication if x then y. There's multiple ways for x to imply y, and those additional meanings do show up in natural language all the time, and we actually do have logical systems to describe them, they are just lesser known.

Mapping natural language into logic often requires a context that lies outside the words that were written or spoken. We need to represent into formulas what people actually meant, rather than just what they wrote. Indeed the same sentence can be sometimes ambiguous, and a logical formula never is.

As an aside, I wanna say that material implication (that is, the "if x then y" of classical logic) deeply sucks, or rather, an implication in natural language very rarely maps cleanly into material implication. Having an implication if x then y being vacuously true when x is false is something usually associated with people that smirk on clever wordplays, rather than something people actually mean when they say "if x then y"