The datasheet for the IRL510A is here;
http://www.datasheetcatalog.org/datasheet/fairchild/IRL510A.pdf
Note, that it says: LOGIC LEVEL GATE DRIVE
that fixes Vgs between 1 and 2 Volts. Guess what those magic numbers are?
It also means the FET will be on when Vgs > 2V, since Vgs Max is what we are concerned about.
Now look at figure 2: At about 2.5 V Vgs, the device can sink about 1 Amp; 10 ^0 = 1.
Note, Vgs leakage current of 100 nA and and input capacitance of 180 pf. What this means is that UNLESS you provide a path to ground for at least this amount of current, the device could turn on by charging the input capacitance.
If some bipolar device is driving the FET, leakage from the Bi-polar device could turn things on and you need to find a place for that to go. That was the purpose of the gate to ground resistor.
As with any port, you have to pay attention to source voltages and currents available, sink voltages and currents available and leakage.
Does this make sense when using N-channel Fets to switch to ground now?