Though played in the United States, it has been an official European Tour event, meaning that it counts towards that tour's money list and Ryder Cup ranking.
But the inclusion of golf at next year's Rio Olympics in August has forced the PGA Tour to bring the Bridgestone forward by more than a month to June 30-July 3, setting up a clash with the French Open.
The French Open, which will celebrate its centenary, is played at Le Golf National in Paris, which will also host the 2018 Ryder Cup.
It is a tournament the European Tour values highly, hence the decision not to sanction the WGC event next year.
"I think they've done the right thing by standing beside one of their mainstays of the European Tour," Clarke told reporters at Whistling Straits.
"They've showed loyalty to the French Open and rightly so."
How much the decision will hurt the Bridgestone field remains to be seen, but it is probable that some players on the edge of Ryder Cup contention will opt to play in France instead.
Northern Irishman Graeme McDowell, the French Open winner in 2013 and 2014, has already said he will probably play in France.
"But the schedule, it's a mess next summer, let's be honest," McDowell said.
"The PGA Tour has had to make some tough decisions. Hopefully, we'll be back to normal the following year. So it's only a one-year deal. Where will I be? I'll probably be in France...
"It's a golf course I prefer. It's a tournament which I want to be loyal to because of how good they've been to me and how much success has been there."
Clarke, who will lead Europe in its defence of the Ryder Cup at Hazeltine in Minnesota next year, said: "If they're close to qualifying on the points list ... it's a tough decision for the guys to make.
"I can tell them what I'd like them to do. But under no means would I try to tell one of my peers what he should do and what he shouldn't do."
(Reporting by Andrew Both in Cary, North Carolina; Editing by Larry Fine)
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