Complex sentence: The "Nugget" staff had a close relationship with Sheriff Behan, but Rule's story, as printed in the "Nugget" the day after the shootout, backed up the Earps' version of events.
Split into simpler sentences: The "Nugget" staff had a close relationship with Sheriff Behan. It's likely that Rule had access to Behan and Rule's story, as printed in the "Nugget" the day after the shootout, backed up the Earps' version of events.