Yes, the claim is approximately true.
From a 1976 study:
Two stages of Vietnam drug use are identified-a period of increasing marijuana use followed by the 1970 influx of highly potent heroin to which 1/5 of the enlisted troops were addicted at some time during their tour. ... Since 95% of those who were addicted to narcotics in Vietnam have not become readdicted, the situation does not appear to be as severe as originally supposed.
Thus, 20% of US soldiers were addicted to heroin at some point during their tour and 95% of those addicted did not become re-addicted after the war and stopped using heroin.
This 2010 paper more specifically mentions only 5 percent of Vietnam war veterans took heroin 1 year after the war. The authors also write (emphasis added):
Eighty-five percent of the men told us that they had been offered heroin when they were there—often quite soon after their arrival...Thirty-five percent of Army enlisted men actually tried heroin while in Vietnam, and 19% became addicted to it.
On 15 May 1971, the New York Times published an article using the term "heroin addiction epidemic" chronicling the high use of heroin (emphasis added; paragraphs not all continuous).
So serious is the problem considered that Ambassador Ellsworth Bunker and Gen. Creighton W. Abrams, the military commander, recently met with President Nguyen Van Thieu on measures to be taken by the Saigon Government, including agreement on a special task force that will now report directly to Mr. Thieu.
John Ingersoll, the Director of the Bureau of Narcotics and Dangerous Drugs, also conferred with Mr. Thieu and other officials and returned to Washington, reportedly alarmed at the ease with which heroin circulates and fearful of the danger to American society when the addicted return craving a drug that costs many times more in the United States than it does here.
The epidemic is seen by many here as the Army's last great tragedy in Vietnam.
Some officers working in the drug‐suppression field, however, say that their estimates [for addiction to heroin] go as high as 25 per cent, or more than 60,000 enlisted men, most of whom are draftees. They say that some field surveys have reported units with more than 50 per cent of the men on heroin.
In the present day, both CNN and NPR write that 15% of US soldiers in Vietnam were addicted to heroin. From the second source (paragraphs not continuous):
In May of 1971 two congressmen, Robert Steele from Connecticut and Morgan Murphy of Illinois, went to Vietnam for an official visit and returned with some extremely disturbing news: 15 percent of U.S. servicemen in Vietnam, they said, were actively addicted to heroin.
Soon a comprehensive system was set up so that every enlisted man was tested for heroin addiction before he was allowed to return home. And in this population, Robins did find high rates of addiction: Around 20 percent of the soldiers self-identified as addicts.
"I believe the number of people who actually relapsed to heroin use in the first year was about 5 percent," Jaffe said recently from his suburban Maryland home. In other words, 95 percent of the people who were addicted in Vietnam did not become re-addicted when they returned to the United States.
To conclude:
Did 20% of US soldiers in Vietnam use "loads of" heroin?
19% of enlisted US soldiers were addicted to heroin "at some time during their tour." 20% is approximately accurate.
Did 95% of the US soldiers who were using "loads of" heroin stop using heroin afterwards?
By 1 year after the war, 95% of the US soldiers addicted to heroin stopped using heroin.
Why is this the case? The environment was different.
From NPR:
It's important not to overstate this, because a variety of factors are probably at play. But one big theory about why the rates of heroin relapse were so low on return to the U.S. has to do with the fact that the soldiers, after being treated for their physical addiction in Vietnam, returned to a place radically different from the environment where their addiction took hold of them.
"I think that most people accept that the change in the environment, and the fact that the addiction occurred in this exotic environment, you know, makes it plausible that the addiction rate would be that much lower," Nixon appointee Jerome Jaffe says.