I have successfully composted the compostable "cold" cups and lids (the clear plastic kind) as well as the "hot" cups which look similar to a standard paper coffee cup.
"Industrial Composting Facility" is merely shorthand for a
well-managed HOT compost pile.
As Douglas states, temperatures over 50*C are required, and if one follows the National Organic Program for composting, you'd be over 55*C/131*F for 15 days.
(We stopped composting them a few years ago; when in a short span of time, we became certified organic and they are not an allowed feedstock, and also a commercial composting service became available to us.)
The biggest trouble that I found was that for the first week, especially the cups near the outside of the pile, they are a round rolling object. "Intact" fruit and citrus rinds were a similar trouble, when turning the pile, they roll off and to the sides, sometimes a long distance.
A lesser trouble was nesting of the cups, which slowed their breakdown slightly, but not
enough to worry about.
After about the third turning, the cups would have split apart at the rim and resembled daisy flowers, and then into small chips.
You really need a pile a cubic meter/yard or more (maybe >10 cubic yards) to easily create and sustain the heat required
and keep the cups buried in the hot center of the pile).