I highly doubt the "contains" label would matter in this case, given that butter IS labeled as such and yet your anecdote stands.

Which is to say, that the label missing from this particular batch is likely to have had zero impact positive or negative on the overall situation.

Yup, and this is why the labels exist. So many people confidently "guess" when asked, and I've had to ask a few times for them to check the label.

Surely the context matters though?

In a culinary context, something can obviously be made with lots of butter and no milk.

In an allergen context it's totally different, but isn't the normal question whether it contains dairy?

I mean, in a regular cooking context, the Americans sound totally correct to me, unless they know you're asking because you're allergic.