There are few actors who could make the receipt of a Facebook friend request feel as cataclysmic as Aldis Hodge does during the unexpected turning point of Tom Shadyac’s fact-based drama “Brian Banks.” As the eponymous lead, Hodge is tasked with carrying the weight of a story that seems too wild and strange to be real: a heartbreaking tale of false accusations and wrongful convictions that literally hinges on an odd olive branch extended via social media. Hodge sells it, just as he sells the rest of an otherwise chintzy film, a Lifetime movie-like drama that falls short of engaging with the many thorny issues it dramatizes.

In the early aughts, Long Beach native Banks was a promising high school football player who committed to playing at USC when he was just a junior. While Banks is a straight arrow with his eyes firmly fixed on his athletic future,...