No, the speed differences were all when good, the fault was when the front passenger one randomly went to zero, the light came on then.
Oh dear, you had to make me go and do maths.......
a quick search found a set of navara wheel and tires to be 255/65/17 which when new will have a diameter of 763mm and a rolling circumference of 2.395Metres
if you wore all 8mm of tread off a tire you would have a rolling circumference of
2.345mm
Which equates to about 2% difference in the rolling circumference between a brand new tire and an completely worn bald tire.
A brand new tire at 60mph, would equate to the completely bald tire reading 61.2 mph
These are not going to be vast differences.
The computer monitors the tires and expects to see those fairly consistent readings thought out the journey. you could expect the pressure to go up and the circumference to go up slightly, but overall things will be pretty stable. However.
But if you pick up a screw and within a hour or two you lose about 10mm of height in the tire wall. The computer will see a significant change that goes well beyond what would be expected from tire wear in a very short space of time.
If you get a puncture and in say 5 minutes the tire wall gives by 1 mm in height due to loss of pressure, it equates to a 0.7% change in the speed of that wheel. So if it was registering at 60mph before that wheel is now doing 60.5mph in a space of 5 minutes.
You could argue that if all 4 tires went down at the same time that this would trick the system into not seeing the problem but there is almost no situation where this would happen at exactly the same time and with perfectly equal loss of pressure.
Also the car knows what size its wheels should be, and learns these parameters when you reset the system. It knows that if you have X number of revs and you select Y gear you should see Z speed at the wheel, if the speed at the wheel is higher, I,e it is going round more quickly due to loss of pressure and a decrease in the size of the overall circumference of the wheel, then there must be a puncture. or the tire fell off.
So no, 4 punctures will not fool the system even if all 4 tires were slashed and you got in the car and drove off, and it is very quick and accurate to pick up the errors.