"I've been told over the last couple of days that a lot of things have been said in the media about how the organization works," O'Brien said, per John McClain of the Houston Chronicle. "Let me say this: Rick and I have respect for each other. We work together and communicate every day. It's a partnership. Decisions are made by the two of us.
"Obviously, they require the concurrence of the owner, Bob McNair. That's how it works around here."
The Chronicle on Monday cited sources with direct knowledge of the situation to report that "O'Brien wanted -- and tried -- to cut Mallett before the Texans ever took the field" for Sunday's 44-26 loss to the Dolphins. Despite Mallett missing the team flight to Miami -- not his first off-the-field incident -- O'Brien, per the report, was overruled by Smith.
Asked if there was a confrontation with Smith over the move, O'Brien on Wednesday said, "No," insisting that the two consistently work out their disagreements.
NFL Media's Albert Breer tweeted that while "gray area" exists in the duo's working relationship, O'Brien houses the contractual power to cut players. Former coach Gary Kubiak, by comparison, did not.
Mallett, for one, would agree that O'Brien had his way in the end.