It's not Warrens fault that after he tweets in his own personal time they called him and put him on air.
Wouldn't that be the NFL Networks problem not Warrens?
Also if he's not a "reporter" why does it matter that he gets his own personal tweets checked by the league, he's not reporting afterall so it doesn't matter.
There is no such thing a "personal tweets" in the NFL, media, or any other organization on the planet. If you comment on a situation ypwhere you can reasonably be assumed to have relevant information or if oyur opinion has an effect on your company, other companies in your industry or peoples perceptions of the goals, structure competence, attitude, etc, etc of them then it isnt personal. Heck, tweeting about your dog can make people you arent serious and god forbid you tweet about politics or religion.