Black coins would be the remaining bitcoins that don't fall into this loop—the unregistered coins operating free outside the system. As the theory goes, these black coins would be harder to maintain and more versatile to use, and could grow more valuable than their traditional counterparts over time.
...which is exactly why such a scheme won't last.
The increasingly restricted govcoins will be effectively be removed from the supply of actual Bitcoins, causing an exchange rate between then that will become increasingly unfavourable to govcoin holders.
You'll see a situation in the US like there is with Argentina - where there is an official (fabricated) USD-ARS exchange rate which virtually nobody uses, and the real market rate which you can only get in the black market. Media scare stories notwithstanding, regular people have no aversion to operating in the black market when it's favourable to do so.
Regulated Bitcoin businesses will whither and die, while their black market counterparts will flourish.
Eventually the institutions holding the govcoins will get increasingly desperate to get the higher black market exchange rate for their coins, so they'll arrange for them to be "stolen" by Chinese/Russian/Martian hackers.