In the first case, the presumption is only that the potential gun owner should be exposed to basic firearms safety. Whether he is safe or unsafe without it is not an answerable question apriori, therefore it is also a moot one. I think we all can agree that safety training is, in general, a good thing, and I also think we can agree that there are some folks not getting any safety training whatsoever.
In the 2nd case, you are correct that I am presuming that safety training would help prevent accidents such as this, although possibly not this particular one. I do not see this as faulty, but rather logical. We all train our children on firearms safety by this same premise.
A person's right to own firearms is not in question. Their right to discharge them in public areas, without having basic safety training is what is concerning. Several years ago, my state implemented hunter safety requirements for new hunters, born after a certain date. Would you consider this to be a violation of fundamental rights?