I would have no fear shipping guitars double-boxed, in a hard case with head, neck, and horns cushioned in the case.
Shipping in a factory cardboard box is tricky. Not much padding. Especially a high value guitar (over $900), I wouldn't do it without insurance. USPS has a 70 lb limit, so not many large packages bouncing around. UPS and FedEx also do freight and super-heavy items so you can run into a big one sometimes (>150lb), though they are processed manually, not on Rapistans or conveyors.
Claims aren't usually a big hassle, but they will likely want pics and the recipient may have to take it to a local site for inspection, depending on value and circumstances. There usually MUST be some outer box damage, or they will get suspicious.
Loose screws as is being described is odd. Unless the neck got "clotheslined" by a heavier load with the body still braced and that somehow stripped the screws?
I would agree that the neck would likely break before the screws got yanked even a little, but I suppose it depends on angles and velocity.
It may have just taken a spill and had the fall broken in a weird manner, near the headstock. The leverage necessary though.....hmmm....