"The world just needs to know that what was accomplished was a once in a lifetime rescue", Anderson told The Associated Press in an interview on Wednesday.
The parents have reportedly only been able to see their children through windows as they recover.
Thongchai said the soccer teammates are in a "very good mental state" and are showing no signs of stress.
None of the boys was heard speaking in the clips shown at the news conference.
Officials revealed on Tuesday that the first eight boys rescued from the cavern were in good health overall and some requested bread slathered with chocolate for breakfast.
Thai authorities imposed a media lockdown during the evacuation, even holding large white umbrellas around the boys as they lay in stretchers outside the cave as they were transferred to helicopters bound for hospital.
Hospital director Chaiwetch Thanapaisal told a news conference that the boys would have to stay in hospital for up to 10 days. Doctors were anxious about potential infections the children could have contracted in the cave.
Thailand's Prime Minister Prayuth Chan-ocha on Wednesday thanked people involved in the rescue. "The best way is not to bother them and let them study".
The boys became trapped in the cave after torrential rain flooded the tunnels, leaving them unable to exit the cave. They were found by a pair of British divers more than a week later.
Getting them out - which involved teaching boys as young as 11 who were not strong swimmers to dive through narrow, submerged passages - proved a monumental challenge. The effort turned tragic on Friday, July 6, when former Navy SEAL Saman Kunan ran out of oxygen and died. "This is clearly a time of grief for the Harris family, magnified by the physical and emotional demands of being part of this week's highly complex and ultimately successful rescue operation".
"We are not heroes". "For SEALs, this is what we were trained for".
The complex mission for the rescuers from Thailand, the US, Britain, Australia and other countries to guide the boys and coach through the cave's flooded passageways riveted people worldwide.
The 12 Thai boys and their football coach have finally been rescued after 17 days underground.
Official help came from Britain, the United States, Japan, Laos, Myanmar, China and Australia, a government document showed.
The mission to rescue 12 boys and their soccer coach from a Thai cave is to get the Hollywood treatment in a movie announced by faith-based production house Pure Flix.
"My wife actually grew up with the Thai Navy SEAL that died in the cave".
"It is with great sadness that I confirm that Harry's dad passed away last night a short time after the successful rescue operation in Thailand", said Andrew Pearce, head of clinical services at SAAS MedSTAR, where Harris works.