After I took my car from them, their service manager called me and apologized. Even though he did not offer to cover the replacement, at least he made sense and was a reasonable person.
He explained that they cannot cover the battery because of low km since last service, but the battery is drained not by that but rather by vehicle waking up all the time, but they have no evidence that vehicle is waking up on it's own - according to the black box, it is woken up by the key (which is should not be the case as far as I know)...
So that makes matters even worse - if it's an issue with a car, I'll buy a new battery, and it will likely die on me again. The manager told me that
they would like to look into that again if I bring the car back. He said he could not guarantee that they end up covering the battery, but it may happen depending on the findings.
Now, I am not pissed anymore, after speaking with a reasonable person, and I do not care that much if I need to pay for the battery - I just want to make sure the car works fine and is not killing battery. So would I have better chances of getting it done by bringing car to them or to another dealer? Seems like they have the background info and showed the interested in rectifying the situation, but as they say, fool me once...