If you read the original study, you're comparing apples to bricks. From Recidivisim of Sex Offenders Released from Prison in 1994 (Langan, Schmitt, Durose)
Compared to non-sex offenders released from State prisons, released sex offenders were 4 times more likely to be rearrested for a sex crime. Within the first 3 years following their release from prison in 1994, 5.3% (517 of the 9,691) of released sex offenders were rearrested for a sex crime. The rate for the 262,420 released non-sex offenders was lower, 1.3% (3,328 of 262,420) So the rate of recidivism for the same crime is higher among sex offenders. The likelihood of being arrested for a different crime is lower (43% compared to 68%).
It should also be pointed out that all these stats are for the first three years after release only.
With that said, your point that recidivism is not a forgone conclusion as the stereotype suggests is correct, Wikipedia just made a hash of the stats.