The difference in strength between 3/32 and 1/8 chain is so small as to be negligible and it is really overbuilt for the application... humans just can't exert the force needed to break a chain and like Mr Stewart, the only broken chains I have dealt with in a long career dealing with chains (industrial and bicycle) 99% of the failures come down to user error.

We run 3/32 KMC or SRAM chain on our tandems and they are subjected to much higher loads than single bikes and don't break.

The only time I had an issue with a chain on my fixed gear was when had been doing a lot of hard fast hill climbs (I was racing folks on road bikes and winning), the chain was fine until I put so much torque into the bike I bent a chainwheel and then the lateral force caused the chain to pop.

I also had a problem with SRAM quick links some years ago and this stemmed from a manufacturing defect in the power link and not the chain.

Avoid cheaply made chains... they aren't worth it.