Hi Exhausted,
Yes … you would need to call them and ask. Most of them probably wouldn’t know but the ones that are focused on more natural materials probably will and will often use wool or viscose/silica inherent fabrics as the fire barrier (see post #2 here).
The options that are available to you would depend on which mattresses you are considering and on the types of materials you are comfortable with having in your mattress. If you are looking for a mattress that has no chemicals of any kind (regardless of whether they are safe) then you would be limited to innersprings and natural fibers but if you are also open to latex (either natural or synthetic) then you would have many more safe options.
While it’s certainly true that there are some very high budget “natural” or “organic” mattresses … there are also many others that use the same materials that are in much more reasonable price ranges so when you are looking at these types of mattresses it can be especially important to make some good “value” comparisons with other mattresses that are available to you that use the same or similar materials that are in much lower budget ranges.
Phoenix