We get asked about this a lot.
The simple answer is yes, pretty much all genuine Panama hats can be rolled, with the exception of some of the more course Cuenca waeves (see our blog about the differences between Cuenca and Monitcristi Panama hats for more info).
The tricky bit (and the big caveat to the simple answer) is really the expectations that the owner of the hat has. Even with a high end Monticristi, once a hat has been rolled it cannot be expected to return exactly to it's original shape without being steamed and carefully re-shaped. Instead, one must expect a hat that is rolled to develop character. In our eyes the imperfections that result from a hat being rolled are all evidence of a life well lived - each crease and wave the memory of some far flung adventure.
The legend we get asked about the most, is whether you can really pass a very high quality Panama hat through a ring or to carry water. We're yet to see any evidence of this (possibly because we don't know anyone who wants to subject their hat to such abuse!). If you have a video (or want to fund the research!) please get in touch!