A nuclear chain reaction takes place roughly over a single microsecond. To travel the ~11 inches of a bomb, in ideal circumstances, a high explosive needs roughly 200 microseconds. It is not impossible that the exact right stuff could happen to trigger the bomb, but it is extremely unlikely - it took the smartest minds in america working together for 3 years to figure out the exact precise timing to prevent a nuclear fizzle and achieve a true atomic explosion. It is, contrary to pop culture, near-impossible to pull off by dumb luck. Mostly you'll just make a radioactive mess.
Right! But that's talking about compressing a plutonium pit in atmospheric pressure--being an extremely dense metal, plutonium will preferentially "squirt out" in any direction rather than compress, if there's a direction it can go in. Therefore, you need to make a spherical shockwave via explosives.
But that's in 1 atm! The initial wavefront of a fission device is going to be conservatively about 4 inches a microsecond (based on early above-ground test photos, modern high-yield devices would probably be faster still). This could very well turn the entire physics package of the secondary weapon into a thin pancake on the blast front, the plutonium can't get out of the way fast enough to avoid compression. This is a totally different scenario than a one-point-safety fizzle. The HE explosives in the second bomb might as well not exist relative to the overpressures faced from the first bomb's detonation.
