His understanding is incorrect. A resistor limits the amount of current that can flow by providing resistance to that current. The higher the resistance, the less current flows. If you know the voltage and the resistance, you can predict how much current will flow.
If the resistor is not there, there's zero resistance; zero ohms. That means there's no resistance to the current, and as much flows as the source can provide. If that current is going through someone's body into the wrist strap, it is bad news.
If the resistor is there, and presents a resistance that's low enough to bleed off static charge, but high enough to prevent shock from common 110 or 240 voltage sources, then we win.
Resistors are not semiconductors, nor are ESD mats.
A resistor doesn't really limit current, because if you increase the voltage, the current will increase.. so the current isn't really limited. It only limits the current at a given voltage is all i'm trying to say.. if you really want to limit a current you have to design a current limiting circuit that will not allow current past some given value to flow.. (i.e. the output current of a voltage regulator can be limited to 1A for example, if the load wants to sink say 10A, the regulator will only give it 1A because it is limited to 1A).. this requires the use of resistors AND transistors
Resistors can be semiconductors.. on chip resistors can be made using P-type-doped silicon.. however. it's more popular to create an on chip resistor using a transistor biased in the triode region.. even better is to use switch capacitors to mimic resistors in transconductor circuits.
but the bottom line is some resistors are indeed made out of semiconductor materials