Hey there, OP here!

Since I was no longer in a contract, and therefore eligible for a device upgrade, I ended up getting an iPhone 7 plus. I'll never know if a newer iOS update would have fixed the problem, the phone is gone now (the carrier bought my 5s for $100 - some kind of recycle program).

Interesting that your friend doesn't recall allowing the update... I don't either (although with Touch ID it happens so fast that I may have inadvertently allowed it).

Hope your friend has better luck (or more patience and can wait for newer iOS updates as the other poster suggested).

Cheers