Hypothetical - Basic Med & Insurance
BasicMed does not completely do away with SI's so your buddy may still need one if he has never had one and has one of the 4 qualifying issues.  



To directly answer your question the insurance company may deny a claim on these grounds as they are somewhat free to deny claims as they see fit. There is some more info from the FAA related to SSRI's here. Remember that basic med is about considering yourself fit to fly and being self conscious of your current state it does not set any protections for you that once you deem yourself fit to fly you actual are. Its a fairly new rule so only time will tell how cases play out in the future relating to issues.