I recently ran into the article Interference in Melamine-based Determination of Cyanuric Acid Concentration from the Journal of the Swimming Pool and Spa Industry published in 1995. The author found that some pools over-reported the CYA level in the standard CYA turbidity test. The pools with overly high readings tended to have high Combined Chlorine (CC) levels. Though several possible culprits for the interference were mentioned in the article, I suspect that it might be urea as this can be correlated with higher CC levels in higher bather-load pools. See the chemical structure of melamine-cyanurate and of urea and see how it could bind rings and therefore a lattice of melamine, though with only half of the hydrogen bonding (so a weaker precipitate).
Fortunately, most of our pools that we test do not have high CC levels, but if we suspect a falsely high reading when the CC is high, adding one drop of sodium hypochlorite to the precipitated sample (i.e. after melamine has been added and precipitate formed from the normal 30 second mixing) apparently resolved the problem. However, I would be concerned that the drop of chlorine might raise the pH too much since the melamine solutions for the CYA test intentionally contain an acidic pH buffer to precipitate more melamine-cyanurate since the precipitate at a pH of 7.0 has a solubility of around 20 ppm. I would also be concerned that the high chlorine level might chlorinate the cyanurate to the extent that it might not produce as much precipitate, even at equilibrium though this is may not be a problem if the bonds for the precipitate are much stronger than that of the chlorinated cyanurate (in equilibrium with chlorine).