In the United States, there is no regulated definition of the term "gluten-free." It means whatever the person making the claim wants it to, or rather, whatever the plaintiff's lawyer can convince a jury it should mean.
The generally accepted definition here at celiac.com is that the product is gluten-free if it contains no ingredients derived from a gluten-containing grain, although there are some exceptions to that rule. Distilled alcohol is considered gluten-free by most of us, regardless of what it was distilled from.
There is a rule proposed and under consideration by the FDA, but it does not rule out a shared facility or even a shared line.
In Canada, a product may be labeled gluten-free if it contains no ingredient derived from a gluten grain. Again, possible cross-contamination is not covered.
The "shared facility" thing is one of my bugbears. Just because the final processing plant does not process any gluten is no guarantee that there is no cross-contamination. Contamination can occur at any point along the supply line, starting at the farm where something was grown. The employees at the "gluten-free" facility may eat donuts from the drive-thru on their way to work.
Even so, a shared facility does not mean that there is necessarily contamination. It only means that the allergen is somewhere in the building. Do you have any foods in your home that contain gluten? If so, you live in a shared facility. Does your family use the same utensils and plates that you do to eat? If so, you have shared equipment.