This is a common one. (full disclosure, I'm founder of a company who's products are intended to help solve the cross-functional team friction problem).
Most likely the issue isn't your co-worker, really. It's more likely that the different parts of the larger team are not focused on the same goals & priorities.
A smart guy once said that ~80% of the friction in teams is due to unclear goals vs. a very small fraction due to intractable interpersonal crap. He pointed out that conflict tends to come from Goals, Roles, Processes, and Interpersonal "stuff" in roughly that order.
What to do? Your guy's manager's solution "you are all professionals" doesn't get at the core issue. But escalating the immediate problem is just going to get people's backs up -- pretty naturally.
The PMBOK (the American National Standard for project management) would point you in the direction of the project charter. See if you have one. If the team has a charter use that to focus people's attention. Since you are referring to the authority your position will be strong. If you have questions about this and don't have a PMBOK, happy to answer them.
Point out to the "all professionals" manager that there is a mis-alignment that has nothing to do with a lack of professionalism. That's a managerial concern that can't reasonably be shucked off.
If you get traction to the idea that the team needs a re-baselining of it's goals, roles and responsibilities again see PMBOK for tools such as roles & responsibilities matrices. See if you can get an Organizational Work Breakdown Structure (also see PMBOK; a WBS that is mapped to groups of people) from someone so you can match against the matrices. What you're trying to do is make the roles & responsibilities concrete. Making things clear is half the battle -- and saying that they are not yet clear is much easier for people to hear than if you just say, in effect, so and so is a bozo.
If you get the "you're asking for so much new work" complaint point out that this is basic stuff that must in some form already exist in someone's inbox or a shared drive or there wouldn't be a cross functional team to begin with. So it's not new work, just needs to be reviewed.
And if you get much further I would seriously suggest finding a project management information system that includes roles, goals, responsibilities, requirements and decision-making in its information model. Something that can keep your team aligned and focused on a day to day basis. That way you can get past today's issue and also not get stuck again tomorrow. (As I said at the top, on this point, I'm biased...)