Can a PCB trace support peak currents?
There is a difference between "peak" and "sustained". 

As others have pointed out, the time matters here. 

When you define the "maximum sustained" current, you gennerally aproach it as steady state system - given a maximum allowed temperature of the copper, and knowing the thermal impedance from the conductor to the enviroment, what is the maximum steady state power we can dissipate in the conductor.

When we talk about peak currents, the key here is that we don't reach a steady state. The copper has a certain thermal mass. This means that we can pump more current through the conductor for a short period - as long as we don't surpass our maximum allowed temperature. The current has to heat up the copper first - if the current pulse lasts shorter than the time it would take to heat the copper past this maximum rated temperature, there is no issue.

This also means that the shorter the pulse, the higher it's value may be. 

When using a resistive model to simulate temperatures, the thermal mass is represented by a capacitance, and the thermal impedance to the atmosphere is a resistor. The current pulse would be a spike in power (thermal current) through this RC filter.