I don't believe this -- neither do you. Thus in my strictly scientific sample of people in the United States (n=2), 0% believe that statement.
"in fact, many people are against letting people out of prison even once they have been cleared!" -- I'd ask you to find the name of one person who believes innocent people should be incarcerated.
The theory underpinning most of these wishes, insofar as these wishes exist and they have a theoretical rather than emotional underpinning, is that there exist a class of offenders who guilty of crimes far in excess of what they have been convicted for, that they have internalized norms condoning things such as violence and theft, and that if released they would continue to pose an ongoing risk to society.
Assuming their original imprisonment to have been the just consequences of one act for which they have been convicted, then the subsequent fantasy imprisonment would be the just consequences of the other acts of which they are (or are forecast to be) equally guilty but for which they have not been convicted.
N.b. The appropriateness and efficacy of these wishes, specific materializations of these wishes, and the way that they interact with other concerns involving the rule of law, the fundamental dignity and rights of Man, and the greater good of society... all of that is not addressed in this post, because the nature of crime and attitudes towards crime in America is a complicated topic and this post is short.
Just look at how the word "thug" is carefully used in rhetoric. The implication is that someone is a criminal simply for being who they are, not because of any particular infraction. Further implied is that people who are "thugs" deserve whatever "punishment" they end up getting, regardless of guilt or even whether they were accused of a crime. The Trayvon Martin controversy brought quite a bit of this to the surface for all to see.
You can find plenty of instances where there was resistance to letting an innocent person out of prison, start by Googling "innocence project".
> I'd ask you to find the name of one person who believes innocent people should be incarcerated.
There are most certainly stigmas in the US about prisoners. There are also stigmas are about certain kind of crimes and that racist and sexist in nature. This is a country in which politicians do not pledge to ensure fairness in the law but to be even harder on criminals.