I genuinely respect when people own up to their mistakes.
I’d greatly prefer a boss who says “look, this isn’t your fault, I wish I could do better by you, but it was my job to protect your job and this is where we are. Absolutely use me as a reference, reach out to me if I can do anything to help you land on your feet”
People really hate when something unfair happens and you try to pin it on them… But when you put down the titles, explain why it’s come to this, and offer to help them find a new job? That’s how you don’t burn the bridge from the other side… It doesn’t even require you to actually take responsibility, you just have to acknowledge it’s not their fault and make them feel you’re not taking it lightly