Hey, I just want to briefly update on that, since you've spent your time writing a response.
In the end, I've decided I feel that they're in the wrong (ethically and legally). I've declined the payment, they've insisted I should pay. I've continued denying the payment and explained that I'm ready to go to court with that. The back and forth lasted for a few weeks (~3), in the end they've already sent me an email that my case will go to debt collection services. I've declined and explained my point of view yet again, explaining that I'm ready to go to the court with that. At this point, they've withdrawn their request and sent me an email that this invoice has been cancelled.
So... that's how it ended. :shrug:
Thanks again for your response! It helped me think about what is right and what is not adhering to the law in the country, and how to proceed.