OK, let's suppose the General is right, perhaps they designed some components with degredation in mind, it's been my belief that Russian's over-engineering everything, but for the sake of argument lets run with it...the one thing that will still be viable is the radioactive material in the damn thing. There are simple enough designs to make it go boom, so that doesn't exactly fill me with great confidence.
Plutonium-239 has a 24,000 year half life. However he could be speaking of the neutron emitter used. If its a simple Polonium/Beryllium design for the trigger, then that goes bad rather rapidly. (Po half life is 133 days) - however if it uses a Fusor, that shold last a really long time.
Of course the more the Pu does degrade, the less yield you will get out of the thing. Fat Boy fissioned approximately 17% of its material, and I can guarantee the Russian bombs were designed to fission much more than that. As you say, even if your trigger is shot, just blowing up the plutonium core would create a really effective dirty bomb. In any case I expect that degrade over time means - over 40-60 years. Not over 10-20.
People like to think its really hard to build a bomb. Its just not. There are laser gasification techniques for Uranium that would cost $10-20K to set up. Yes, it would take over 2 years to obtain enough material for a Bomb using that menthod, and you sure couldn't build an arsenal that way (wich is why most people are still using centerfuges) - Just bombaring Thorium (very common and easy toget element) with Neutrons creates Protactinium which can be chemically separated and decays into U233. Unlike our Pu bomb above, U233 will tend to decay more rapidly so you would need to use the bomb shortly after making it - so its not used in making National arsenals. However, people with other purposes may not care about the increased radiation risk, or having to use it quickly after its made. A simple gun design ( round peg, round hole) is sufficent to set it off. Little boy used this design and it was so simple and foolproof, the design was tested over Hiroshima. Its so easy,
a child could do it Little Boy's yield was really low, .038% fissioned. By today's standards a really poor and ineffecient design. Still seemed to do the trick at the time though, didn't it?