She's not deflecting blame. For one thing, it's not Merkel that made the decision. Secondly, the blame would have been less if the government stopped the complaint. That would have been the easy way out.
This is really terrible news for Germany and the EU as a whole. Merkel has said "this is a bad law and we have the option to ignore it, but we will prosecute anyway". Who rules Germany now, exactly? Is it Merkel or is it Erdogan? And if it's the latter, which is what it looks like, then how much influence does Turkey have over the EU as a whole?
Nor is Erdogan calling any shots, because he is only using an option that German law provides to any organ of a foreign state. To any Human Being actually, considering that there are cases of personal defamation pending.
Nothing special about Erdogan, except that he is exerting that option rather spectacularly to his own detriment.
The sad thing about this issue is that obviously a lot of people don't bother to appreciate the complexity of the issue and want to frame it as a question of who is in power and who is calling the shots.
If you don't want to be ruled by dictators, start recognizing law and institutions at work, rather than attributing everything that happens to the power and will of singular persons.
My eyes keep glazing over... can you reword without the triple negative?
So yes, the government had to give explicit permission to prosecute in this particular case.
The gov't could have honored the law by just saying "we don't consent to the prosecution", they did not however, and Merkel as the head of the government has the responsibility for that decision; whether you agree with the decision to prosecute or not.
PS: German media is reporting that according to Steinmeier, German Foreign Secretary, the cabinet had a tie when voting on prosecution or not, with Merkel's vote breaking the tie in favor or prosecution.
Another important consideration is that exercising the right to deny the prosecution would have taken away power from the judiciary. Germany is in the process of making this point to Poland and Hungary, where the independence of the judiciary is under attack. A denial would have weakened that argument a lot.
Of course the gov't has a moral and also legal obligation to consider the request, consideration does not imply they have to follow the request.
If the government made a new law requiring gov't consent before prosecutions or if they tried to hinder a prosecution under any existing law not having such a "government must consent" paragraph, then you might have a point; here however, you do not.