Why it Might be True :
In the seedy world of professional boxing, Liston was perhaps the dirtiest and most mysterious guy in the ring. No one knew, including Liston, when or where he was born. Liston had done time and apparently had underworld connections, including having his contract owned by notorious and prominent Mafiosos.
Because of that, there were rumors that Liston bet against himself because he owed money to the mob and really didn't feel like getting fitted with a pair of cliche cement shoes.
Artistic rendering of Liston's Mob Boss.
To make things worse, apparently Liston had another group to fear: the Black Muslims who supported Ali. The word, coming straight from one of Liston's trainers, is that Liston was so petrified of being murdered by the group that he decided it just wasn't worth it to mix it up with Ali. So taking the dive may have killed two birds with one stone.
Or not, since Liston died a mysterious death (the cops declared it a heroin overdose, but he barely had any in his system), causing some to speculate he was murdered. Man, if you can't trust Mob bosses and violent extremists, who can you trust?