You make a good point -- my answer actually lacked nuance. States are slowly allowing for post-conviction review of factual matters. Sadly, these steps usually

You make a good point -- my answer actually lacked nuance. States are slowly allowing for post-conviction review of factual matters. Sadly, these steps usually only start once the regular chain (primarily law-based challenges) of appellate review is complete, so it can be five or ten years before you get to make your case. A lot of this stems from the swathe of exonerations that happened once DNA was introduced and freed a large number of provably innocent people previously found guilty.