Part of the problem is that when the taps get turned on it doesn't irrigate the ground like rain would, the spread is inconsistent and often creates false ground which is why they always prefer nature to do the watering.
If you ever see the process in action you might be surprised, it isn't a particularly efficient rotating sprinkler system like you'd have in a garden, it's more a basic hosepipe left in a single position blowing in the wind so all the water goes in one direction, they then move this along the course an intervals, it really isn't scientific at all so when they call the official going it is more likely to differ greatly across the course which it wouldn't if it rained.
I still can't believe in this day and age racecourses don't have some sort of professional sprinkler system as well as covers that cover the entire course (these could be built into the rails and rolled out when needed).
Yes there's a cost but there's plenty of fixtures lost to waterlogging every year....