I've heard hundreds of times that ammo will last if stored properly, usually defined as a "cool dry place".
There used to be an FBI regulation that every assigned vehicle (called a Bu-ride or Bu-car in the parlance) had to have a box of service handgun ammo in the glove box. This was checked once a year and the box was dated and initialed for no reason other than JEH said to do it sometime before 1972.
One year I volunteered to check all the ammo boxes, and also convinced the division primary firearms instructor to replace all the ammo with fresh ammo. He could not have possibly cared less, but humored me.
Almost all of the boxes were .38 Special 158 grain LSWCHP, with a healthy smattering of Federal 147 grain +P+ Hydra Shoks. Even guys that had 9mm guns had .38 ammo in the glovebox, since no one in the history of the Bureau had ever actually needed that ammo, except to get past inspection.
The PFI told me to shoot it up, so I did. I retired 20 something years later, and I still am.
Some of that ammo was ten years old then, sitting in cars that got to over 100 degrees above to well below zero. Then I had it in various garages and unheated out buildings over the years, in climates from Montana to New Mexico.
It always works fine. I don't think it matters how you store ammo.