As no POWs have been recovered alive since Operation Homecoming the truth of the matter is up for debate. MIAs are continuously being searched for and recovered by the DPAA. I have not seen any reports of remains being recovered where the deceased expired after US involvement ended, so at this time there is no concrete evidence any POWs were not returned.
The Vietnam War was unlike previous wars fought by the US. There were few large-scale engagements between forces, and US doctrine did not involve holding terrain for extended periods of time. To give an idea of how dense the jungle was, John Plaster's book abut MACV-SOG also goes into detail about ambush and capture missions where men would position themselves mere feet from an active trail, remaining completely undetected for long periods of time. The Vietnamese tactic of "hugging the belt" to negate the advantage of US air power meant that you were often feet away from the enemy in combat. All of this made casualty collection and accountability extremely difficult. Many of the men who went missing in Laos and Cambodia have not been recovered to this day, such is the difficulty in finding remains in the jungle.
In addition, the social climate at the time engendered a great deal of distrust of the government (eg: Watergate in 1972), so it is not hard to imagine civilian and soldier alike questioning the statement that there were no American POWs left in Vietnam, especially after Vietnamization and Nixon's "Peace with Honor" made it seem as though the leadership was very eager to wash their hands of the whole thing.
In the early 80s the CIA thought they had found a POW camp in Vietnam in some photos taken by an SR-71. A mission was prepared to go in and rescue the suspected POWs, but before it was launched a retired Special Forces officer named Bo Gritz announced his intention to launch his own privately funded POW rescue mission in SE Asia. That Gritz was receiving help from the Intelligence Support Activity furthered conspiracy theories that agents within our own government did not want POWs found. This event became fodder for Hollywood, with several movies in the 1980s dedicated to POW recovery efforts.
Ronald Reagan, who was President at the time of the above incident, did not seem to put much stock in the live POW theory. In a radio address he gave in 1986 he discusses the POW/MIA issue as one of recovery rather than rescue. The distinction is important.