Some people apply for asylum based on persecution other than government. Some countries are aware of this and issue passports to their citizens even if they have asylum status in US.
Ummmm... I am inclined to argue with this point. It is called "political asylum" for a reason. If one is not under direct persecution of their government, then they are under persecution indirectly. By this I mean political asylum covers both active and inactive government actions. For example if you are gay and your government does not directly jail or torture you, but will also not stop others from harming you based on your sexual orientation (e.g. public bashings and beatings, etc.). Or you belong to a minority tribe and the government does nothing to prevent other tribes from abusing you. In these cases it is easy to say "the government had no direct involvement", but does that mean they aren't involved or responsible? I think not!
Bottom line, there are very few and rare instances in which a government is not somehow involved in asylum cases. After all, any government is responsible for all goings on within their territory. And if there was justice one would seek it with their government rather than seek protection from a foreign one. Hence why it is called "political asylum"!