This doesn't sound right.
They can refuse for any legal reason. In other words, they can't discriminate. So the real question is whether the state they're in has disability/mental health as a protected category. And "disability: physical/mental" is in fact a protected class in Missouri.
So the question is, since the gun store owner can't discriminate based on mental health (except where the law allows), can the gun store owner refuse to sell based on the phone call which notifies him of a history of danger, as opposed to the mental illness itself.
I suspect the court will discuss it and we'll see.
But until the laws change, generally speaking, if you have not been committed, but are mentally ill, not only are you allowed to buy a gun, but in most states gun store owners are required, by the same laws that require cake bakers to bake cakes for gay weddings, to sell them a gun.