If someone is upset with you because of something that isn't your fault, do you still apologize?

I apologize unless it's an egregious accusations. I feel like the soon I give em the "my bad, you're right" they'll see how pointless it is to argue with me. I've been told not to do that tho...
If someone is upset with you because of something that isn't your fault, do you still apologize?
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