Counterpoint: if we tried to build all software using the same rigorous and "clever" processes that aerospace engineers do, almost nothing would ever get built. It's a different process because it's a different field, not because aerospace engineers are fundamentally more clever.
Have an aerospace engineer cow-orker; one favorite quote for why he works in enterprise software is, "Because this flies and that (pointing at an Ares-1 mockup) doesn't."
On the other hand, there's nothing "engineering" about software engineering.
And I would tend to agree with your second point. We might occasionally borrow some formalism and organizational structure from our engineering cousins, but it's different in enough ways that it probably shouldn't bear the same moniker.
Signed, Not an aerospace engineer ;)