Those situations are not equivalent. When skidding, one unweights the rear wheel to initiate the skid. When people pedal forward, they do not do this.

Some cyclists can deliver 1800 Watts. Their chains don't break. It's highly unlikely that a broken chain is actually due to stresses caused by typical urban fixed gear riding. It's really hard (i.e. impossible) to break a properly installed chain with no manufacturing defects.

I think the original suspicion of too much slack is probably correct. Originally I suspected the OP reused a pin on installation (don't do that with 9/10-speed chains), but he used a Masterlink.