One does not have to single out "the Peltier case" to see that it is difficult to overturn a significant guilty court verdict. There are many people who face that same dilema, in and outside of the USA.

That being said, a legal process does exist, and people do get court rulings overturned (or at a minimum get freed). This occurs more often where a very compelling case exists.

I suspect that cases involving clear and coldly executed death (and, especially the killing of law enforcement officers), make such appeals even more difficult, in all countries. But, that should not be a surprise.

If a person is seen as violent (potential violence is not always seen to be mitigated by being locked up in jail), associated with other crimes, or a member of an extreme political movement, would anyone expect freedom not to be even more challenging to achieve?