Nice try, Soviet Propaganda Ministry.
Nobody volunteered, this was soviet russia. The 'bio-robots'[1] were all culled from reservist regiments and most of them were absolutely scarred shit of going in and cleaning up.
Even the miners who worked to re-support the foundation were never 'asked' - they were simply bought onto the site and dumped there.
The full time military units never went anywhere near the reactor - that was for the reservists. They needed the military units to keep everybody else inline.
As a person who's family survived eastern euro communism, I can tell you that your view of it is greatly, greatly skewed and straight out of what they wanted people to believe.
there was no 'please' or 'thank you' or 'yes' or 'no' - there was say nothing, or be missing.
checkout this excellent doco about the biorobots and the cleanup: http://www.youtube.com/watch?v=t4vMTdSAm1w
[1] Why they were called biorobots is chilling. The roof of and surroundings of the reactor had to be cleaned up. They bought in robots, but they would break down due to the high radiation exposure. It is estimated that on the roof it only took 40 seconds of exposure to receive a lethal dose. When the robots broke down, the army response command bought in reservists who they dubbed the 'bio-robots'. These guys were given sheets of lead to stick to themselves to provide some protection, and then sent up to the roof holding a shovel in 1 minute intervals. Some of the bio-robots made 5 or more trips - there were almost 200,000 of them in total, and it is estimated that over 25,000 died right afterwards, and the majority are now disabled or dead. All of the official reports were downplayed and the incidents covered up until after the wall fell.