Reconciliation is restoration. Just as a furniture maker cannot restore a beautiful cabinet without careful inspection, understanding the exact nature of the damage, and patient, focused work, the wrongdoer cannot restore the relationship that they broke without carefully inspecting their own thoughts, understanding the exact nature of the damage those thoughts lead to, speaking out loud what they did and have now learned to the person they harmed, and patiently working to incorporate those lessons and rebuild trust.
Yes, it’s the wrongdoer who bears the burden of reconciliation, for it was their bad thoughts and selfish actions that broke the relationship in the first place.
When the wrongdoer offers to repair the relationship, they’re acknowledging that they’re responsible for breaking it and thus for restoring it. This is truth.