No, there is no exception. If a belief is based upon external evidence, then it is not self-evident.
Example: It is self-evident that a bible is evidence of a bible. It is not self-evident that a bible is evidence that God exists.
Example 2: It is self-evident that complexity is complex. It is not self-evident that complexity means something created it.
Simply that I acknowledge that you believe something, doesn't necessarily mean I am acknowledging what you believe.
Well that's the standard definition.
Why not just admit your wrong and save yourself from further embarrassment?
When I am right, as I am, there is no embarrassment. When you have been laughed at as long as you have been, you can't feel the embarrassment, can you?