Most tire manufacturers, good or bad, aren't going to participate in anything like that because they have no control over the validity of the test procedures or apparatus.
For example, we did machine testing using roadwheels that were set in place with cranes when the machines were assembled. Weights measure in tons. The purpose was to make the radius of the contact surface as large as possible, with larger tires needing larger radius wheels to produce useful results. The ideal tire test machine would have a flat bed and no radius, but there are more than a few impracticalities in that design that are somewhat tough to overcome. In any case, tire test machines capable of producing useful and repeatable results aren't commodity items widely available. Something upward of a $million would be my guess for something useful for passenger car tires, and no magazine is going to spend that kind of money to produce an article in one issue of their rag.
The typical magazine tester would most likely run his test using the most widely available piece of test equipment. That would be a roller type chassis dyno, and the results it would produce, due to the comparatively small roller diameter, would be useless. It'll destroy any tire you run against it, but the results are no more predictive of real world conditions than if you stuck a stick of dynamite in each of a dozen unmounted tires and then claimed the one that survived the blast to the greatest degree was the best tire.
At the bottom line, testing tires is pretty simple. Figuring out HOW to test them effectively is the tough part. Effective analysis of the results is another tricky deal too, and there's very little about it that's intuitively obvious.
All the major manufacturers do competitor testing to see how they're measuring up against the competition. We used to regularly swap a new set of our tires to a car dealer for a set of competitor tires right off a new car on his lot as a method of making sure we were getting representative examples of what the carmakers were getting.
We took all sorts of precautions to assure equal test conditions in competitor tests, regardless of whether they were machine tests on on-highway wear test, or on-track adherence tests. Always assumed our competitors took the same sorts of precautions because massaging the results to favor your own product does nothing to enhance your investigation of the competitior's position in the quality chain.
For any tire manufacturer to supply tires for testing, along with implicit acceptance of the validity of results, to any organization lacking a solid capability of legitimate testing would be foolish. The only way to get legitimate 3rd party results would be for the magazine to purchase tires at the retail level from the various makers, and pay someone like TRC (contract vehicle component testing company) to run the tests. They might be able to buy the tires, but they couldn't afford the testing.
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