This sounds too ridiculous to be true. I'd be more inclined to believe that it's a gambit to flush out an intelligence leak rather than an inability to find their own $160M plane.
You'd be surprised to learn then that the United States has lost several (6, last I knew) nuclear weapons over the decades. https://www.bbc.com/future/article/20220804-the-lost-nuclear...
> The US Department of Defense has officially recognized at least 32 "Broken Arrow" incidents from 1950 to 1980.
https://www-tc.pbs.org/wgbh/americanexperience/media/filer_p...
> Unofficially, the Defense Atomic Support Agency (now known as the Defense Threat Reduction Agency (DTRA)) has detailed hundreds of "Broken Arrow" incidents.
https://en.wikipedia.org/wiki/United_States_military_nuclear... ("Broken Arrow refers to an accidental event that involves nuclear weapons, warheads or components that does not create a risk of nuclear war.")