The Coca-Cola company manages to supress an entire film because they didn't 'authorize' an image of a Coke can in it.

As the main character says, "My God, what a testimonial!"...

Any idea what the legal rationale could be? I read the article, but it was pretty uniformative. Surely Coca-cola is a matter of trademark, and I believe trademark law allows the use of the trademark by others, for example in works of fiction and in general in settings where it does not result in consumer confusion.

The legal rationale in 'trademark infringement'. But that is a 'rationale' in every sense of the word. You are right - the legal claim is completely bogus. However, this is a legal threat is ALWAYS used in the entertainment industry, but is never challenged because most film studios are too risk adverse towards litigation costs.

What they don't realize is that in the long run, they pay far more to maintain a 'legal affairs' department to get bogus 'rights' and 'clearence' of products and brand names that happen to appear in their films. As a result, a grotesque business culture is sustained and nutured whereby fair use and free speech is ignored at the expense of corporate interests. That business culture from the entertainment industry has bled over into aspects of the legal culture - which is why fair use is under unprecedented assualt. But if more filmmakers insisted on standing up to this and forcing courts to take a look at it at the appellate level - I am confident that it could be rolled back. But thus far, nobody wants to do it.

To quote Judge P. Boren from the California Court of Appeals:

"The industry custom of obtaining 'clearance' establishes nothing, other than the unfortunate reality that many filmmakers may deem it wise to pay a small sum up front for a written consent to avoid later having to spend a small fortune to defend unmeritorious lawsuits such as this one."

[Polydoros v. Twentieth Century Fox Film Corp. (1997) 67 Cal.App.4th 318]

Coca Cola should be happy with this film. Jesus would never drink such a toxic product, so this is an unmerited endorsement -by proxy. If they were smart, they would shut up and capitalize on the holy pitch.