There is no problem using a 3/32 chain on fixed gear bikes. They're no weaker just because they can flex to the side more. I swear I've seen Sheldon (and others) discuss this exact topic. Ask how many people have snapped their 3/32 chains from regular use.
I wasn't aware they even made 3/32 track chains, which is why I assumed that "track" drivetrain parts are all 1/8. That's what I get for assuming.