Correct. But what I care is to whom the Chinese public will go to next time.
The western media have scored twice on the missing of Qin and Li. Say it was NYT who was the first to report both stories. Now imagine this. Another high ranking front-row member of the central government had been missing from public for a few days. NYT started running a story speculating if the person in question had defected to the US. Would you believe it or call it bull? What would you think of the Chinese public's take on the story? What if that person were not able to resume his duty for a few weeks more?
The rumor and other leaks were spreading around China long before Western media hyped the incidents. Most forums or wechat groups were talking about these two topics for sometime especially after many not anti-China insiders didn't refute such claims.
Western media is irrelevant in this matter. Most mainland Chinese trust their own network more than both Western media and Chinese media. That's why social media and other platform were infiltrated by so much misinformation as it is the most effective way to instigate fake news and brainwash people.
To answer your question, Xi and a few top officials didn't show up for a few days or weeks. Rumors started flying, Western media reported and hyped the news. Xi showed up and rumor died down. Another example, three gorges collapse rumor showed up every year during the raining season and every time Western media picked it up and then died down after flooding season ended. See the pattern.
Such rumors were pretty effective for Western audience but not so effective for Chinese audience. The reason is that Westerners don't pay much attention after all the hype is over as it doesn't concern them and anti-China is ingrained in their thinking. However, such rumor could be counterintuitive for mainland Chinese such as three gorges. After crying wolf for three times, people just don't trust you anymore even if you are right occasionally.
You don't fight fake news or conspiracy theories after they have shaped up. You reduce the chance for them to spawn. More importantly it's about how the Chinese authority should maintain its position as the authoritative source of information on issues that matter to the Chinese public.
Most mainland Chinese don't concern that much about arresting and indicting high profile government officials. Unlike the West, mainland Chinese are used to such high profile arrests. The process is first arresting for interrogation, then strip of official position and kick out being communist member, and lastly formal criminal investigation and indictment.
For interrogation and evidence gathering, the Chinese government would maintain silence and denial until enough evidence for next phase which usually takes a few weeks. For government officials, a formal announcement would always make. The problem is that for anyone who got charged, there probably a few more that just got interrogation for a few days without charges. Unless, a criminal charges were warranted, it might not be the government and public interest to make an announcement. So between a few days to a few weeks, this is a gray period that rumor would spread.
What is truly hurting Chinese government's credibility and authoritative is its inability to combat rumors about government's coverup and collaborate with criminals. Most often, a minor case of suicide and then rumor started flying and when evidence is presented to the contrary the perpetrators move to the next story. Fighting rumor is always a lost cause.