It also seems Putin has heavily criticized the UK for arresting Assange, claiming is the evidence that UK doesn't have a real democracy. I have no idea what's going on: the only explanation I could come with is that Putin is trolling hard.
The claim sounds weird to you because you are considering how the claim sounds to a citizen in a western democracy. The truth is, Putin really couldn't care less about that. The remarks were absolutely aimed at Russian citizens -- see, we are not that bad in comparison.
There appears to be an ongoing low-level diplomatic conflict between the UK and Russia since the FSB guy who was killed on British soil - I'm sure that plays a part in his comment.
The "conflict" has been going on ever since the Berezovsky received asylum in the UK. He continues to fund activities against the Russian government, but the UK refuses to extradite him. The reason all the politicians in the UK freaked out over Litvinenko is that it puts London's reputation as the leading safe haven for defectors/dissidents/mafiosos and their money in doubt. A big reason that London is the world's financial capital is that it is also the world's money laundering capital.
Of course none of this applies to people like Assange because they don't have any money or come from countries the US doesn't like.