Panama Hats are made in Ecuador, not Panama.
People building the Panama Canal wore hats from Ecuador that may have led to the hats being called Panama Hats..
Theodore Roosevelt wore a “Panama” hat when visiting the Panama Canal construction.
The best Panama Hats are made in Montecristi. The palms that form the base for the hats grow around Montecristi and many high quality hats are woven in the area. Though some are finished there it is more likely the hat has been finished further south, often in Cuenca.
Panama Hats are “made” in several places. The raw material is grown in one place, boiled and dried in another, woven and finished in others.
Panama Hats are not made from straw. They are made from toquilla palm.
Good Panama Hats can be rolled up. But no supplier of genuine Panama Hats recommends that you roll up their hats. Indeed, one we spoke to in Quito has stopped supplying balsa wood boxes unless a purchaser really insists.
You can roll and squash crocheted hats.
UNESCO has recognised the legend through adding the traditional weaving method to its list of of World Cultural Heritage items.