High nitrate levels do two things to inhibit coral growth: 1.) Grow algae which soaks up phosphates leading to phosphate deficiency 2.) Interferes with the symbiotic relationship where the coral passes nitrate to zooxanthelle and the zoox in turn gives the coral sugars to grow.
There are hundreds of white papers on this subject, phosphate deficiency is even the cause for many coral reefs dying out. In one experiment, coral growth was examined at a range of phosphate levels. Coral & polyp growth was the strongest in the largest phosphate level of .5ppm.
Moral of the story, watch your nitrates, not phosphates. Algae can only grow up to the nitrate level in the tank, but then can't consume more phosphates.
You of course need trace levels of nitrate for the coral to pass it to the zooxanthelle but that is a very very small amount.