That's mostly correct. You can't breed Pu-239 without also breeding a little Pu-240, and you basically can't get it out of the Pu-239. Pu-240 has a very high spontaneous fission rate (atoms occasionally just fall apart, often releasing a neutron or two). At the levels present in a few kilograms of Pu, there's a random neutron every microsecond or so.

For a gun-type design, it spends a fraction of a millisecond in a configuration where a chain reaction is possible but generates a dud. And the Pu-240 spontaneous fission makes it very likely that such a dud chain reaction will happen.