The person holding it.
Clearly that isn't the whole answer. Canon have a line of cameras aimed at professionals with a distinct set of features, which appeal the kind of people, who take pictures for a living.
This is the point that I'm getting at. For example, the 5D series camera I have considered to be the ultimate wedding photographer's camera. Now along comes the 6D. It is generally plastic, it does not have all of the bells and whistles that the 5D series do, but it does have some that the 5D series do not have. The 6D can also be considered a fantastic wedding photographer's camera. So why would the 6D be less of a professional camera than that of the 5D?
My theory is that it is the professional who sets the criteria for what they consider to be professional grade equipment. They are the one's making the money and most professionals I know, in any profession, will spend only the right amount of money on the right tool to do the job.
I recently went with a wedding photographer to a shoot to be an unpaid apprentice to see what it's all about. I was stunned when he whipped out a Nikon 5100 and a kit lens, and that was all that he had. It went against all that I believe and had read in the forums here on CR. There was no backup, it was a crop sensor camera with an average lens. He didn't have a flash either. I was expecting at least 2 cameras, a few lenses in the f/2.8 or larger range with one being a 70-200, another being 24-70 and the last a macro of some kind. Maybe an assortment of flashes and portable modifiers. At the end of the day, though, the bride was happy.
Now I still would bring at least two cameras to such an event for redundancy purposes, but looking beyond that - the bride was happy. That is when I started to question what I believed a professional level camera should be. I can see the build quality being a valid differentiator, but I'm failing to see anything else at the moment. Even support levels are questionable to me since that is a choice that, in the example given above, CPN does not want to offer the level of service to a T3 that they would provide to a 5DIII.
I don't believe there is a right or wrong answer here. From the responses so far, it appears that "professional grade" falls to the perspective of the professional and what they value in their respective tools. This was a fun thread to post - thank you for all of your responses.