According to the explanation given by Priest Moli of the Revelation Institute, Prince Long Qing suffered a cold on his way from West-Hill to Chang'an, and he had been recovering from it at the Peach Alley all this time, for which he hadn't been able to visit his brother earlier. Knowing that His Highness the Crown Prince was to make his return tomorrow, he forced himself to come and meet his brother despite not having fully recovered from his cold.
Being such an important figure of the Judicial Department of the West-Hill Divine Palace, and powerful enough to be on the verge of entering Knowing Destiny state, no one would believe that a cold would have any effect on him. Everyone knew that, Prince Long Qing simply didn't want to see the Crown Prince too soon. Nevertheless, if that was the excuse given by West Hill, they had no choice but to accept it as it was, unless they wanted to engage in direct argument, which obviously wasn't the case given the circumstance.