Once again: ICANN has absolutely no influence on the operation of independent DNS servers. If they want they might put them on a blacklist and ban them from the DNS tree. But the direct access over a browser plugin or a direct entry in the DNS settings would never be affected from an ICANN ban. Only possibility for a government would be to advise the ISP to disconnect the DNS server. If you're operating several servers at several locations you're independent from any government - until they get it to advice or control all ISPs of the world. This would be a hard job
Of course there would still be the technical possibility to advise an ISP to blacklist a specific DNS server for connections from outside, means to block normal internet users from using this specific DNS server. I never heard about such proceeding, in this case the user might change the ISP and/or the DNS server. But all this are just theoretical extreme cases. Also the moon might fall onto earth and burst it to dust.
But what does it mean when you say independent DNS servers?
If a server is located in x geographic district then it is ultimately under the control of x country.
If some small part of the process is under the full control of x country then the whole network is subject to the influence of x country.
Suppose in this most recent case the websites illegally trading oil had been outside Icann authority. There still would have been a hundred ways to remove the website, it just would have been a little more difficult.
It seems that the only way to make a secure internet, in which no part of the DNS system is vulnerable to outside politics, is to have the entire system geography based.
In that case a country could prohibit access to another countrys domains, for example the U.S. could prohibit anybody in the U.S. from accessing websites that illegally sell or trade oil, but there is no way short of military to actually prevent such communication about oil sales between foreign groups.