Chase and their insurer will not provide anything unless you get their form filled out, which includes a section for the doc to complete and sign. Either way, even with that, if AS gives you a credit, they will also not give you reimbursement until that expires unused (though they will reimburse any change fees you are assessed - again, once you have the proof that the traveler can not travel based on the advice of a medical professional). They will reimburse for any change fees after those are paid, again with the proof.

don’t know how AS works, but I typically fly UA, who doesn’t have change fees and provides full credit as long as you cancel your segments prior to travel - we also travel enough to use before expiry so don’t have to deal with insurance for that. So trip cancel is almost useless for us because of this since post-COVID change fees are nothing (trip delay is something that we’ve used, though). If AS does similar, definitely get what you can for that, or whatever they might give you, as if you’re unwilling to get the sign off from a doc, it’s better than the nothing you’ll get from card coverage.