He wouldn't have to post anything on social media. His agent would just let it leak to a reporter that the reports are false and Carr has no desire to leave. That's how these things are done.
And it's not Moscona. It's Underhill who would not put his reputation on the line repeating this story many times unless he had very solid sources to back up the story.
I know you and others don't want this story to be true, but it is bordering on ridiculous to continue to deny it at this point.
It doesn't mean he still wants out or that he won't be the starting QB this year. But it's clear that at some point prior to the restructure, he requested at trade.