I am not so surprised to see this news. Because the adoption of Bitcoin is growing day by day. In mostly payment, Bitcoin is also used as a payment method. Bitcoin is the best currency in the world. But if is only available even you are connected with the internet. So, if you don't have internet access you cannot access your wallet
I'm surprised for the luck the OP saw in that clinic because, he said not that the clinic is accepting BTC from patient payment in the clinic but he seen the doctor with BTC logo that gave him the confidence that the doctor may have knowledge of BTC which the doctor confirmed that he has and, his problem was solved for him to pay for his wife delivery in the clinic which the doctor accepted to do it on behalf of the clinic.
There is no magic you can do to have access to your wallet without internet network in that geographical area which is the luck the OP experienced from the transaction he made to the doctor with BTC for the clinic management to allowed him to go with his family
because he has paid the clinic bill.