I'm surprised the conference doesn't provide tooling to validate all references automatically.

How would you do that? Even in cases where there's a standard format, a DOI on every reference, and some giant online library of publication metadata, including everything that only exists in dead tree format, that just lets you check whether the cited work exists, not whether it's actually a relevant thing to cite in the context.

Sorry, but if someone makes a claim and cites a reference, how do you verify "is the stuff correct" without checking that reference?

Those are typically things you are familiar with or can easily check.

Fake references are more common in the introduction where you list relevant material to strengthen your results. They often don't change the validity of the claim, but the potential impact or value.