One hates to have to leap to the defence of Brailsford, but he did not say he doesn't listen to or value criticism. The key part you're overlooking is 'someone else's narrative', or self-serving criticism. I'm sure those who fully value informed criticism themselves can see the importance of this qualifier and how its presence means the statement doesn't mean what you're saying it means."I would never judge myself by someone else’s narrative"
SDB September 2020
Translated out of spin-speak
"I don't listen to / value the criticism of anyone."