In theory, these answers are vaild, however, in practice you will find that the absolute operation of a transistor near Vt/Vth is more of a grey area than black or white.
When you simulate this transistor, your are probably using a model. The real question is how does this model provide a value for Vt/Vth. In most cases, different companies/foundaries will overspecify the satuaration "Is" current for the transistor turn-on voltage (ie @ VT) roughly between 1e-15 -> 1e-10. In orders of magnitude this is a huge difference ?!?!?
In my experience, you should be concerned with two issues and include some margin. Eg......
for SatMargin use Vds-Vgs+Vt > +/-30mV
but also important is VDSAT = Vgs-Vt > +/-10mV to avoid pinch-off
Hope this provides more depth to your problem