Well, yes, because 99 percent of people in general know that butter is made from milk, and that includes 100 percent of the people who might visit my house. And if I did somehow have a visitor so profoundly broken that they didn't know it, I would notice that.
Also approximately 100 percent of professional cooks know that butter is made from milk.
Grandparent poster is just throwing all the hypotheticals for the remote chance of "But what if, and if, and if, and if...".
I am now curious about that "approximately".
I certainly hope that anyone cooking food at a restaurant knows that butter is a milk product.
The butter in my fridge right now doesn't have labels on it. Because I take it out of the box it comes in and put an individual stick in that little covered shelf at the top of the door. My understanding is that that's what that shelf is for, so I suspect that this is a fairly common thing to do.
EDIT: Again, people are trained to trust the labels – not to parse the marketing. That's why they exist. If someone in a kitchen says "grab the dairy-free butter", the most accurate way to check is to glance at the "Contains" label. Once that trust is broken, the label is useless.