Hi Shawn, it depends on when the ACTION tooks place in the past.
These are two different past verb forms:
1) PASSATO REMOTO (Lui disse che...) >> "REMOTO" means remote. You can use this past form when the action/the fact tooks place a long time ago (the last year, ten years ago, when he was a child, etc)
2) PASSATO PROSSIMO (Lui ha detto che) >> "PROSSIMO" means near. You can use this past form when the action is happened in the recent past (yesterday, two hours ago, the other time, the last time, etc).
There is another important past verb form : 3) TRAPASSATO PROSSIMO (Lui aveva detto che..)
When you use the PASSATO REMOTO (firts verb) you should use TRAPASSATO PROSSIMO after (second verb)
Ex: Lui disse (PASSATO REMOTO) che aveva comprato (TRAPASSATO PROSSIMO) una nuova auto.
When you use the PASSATO PROSSIMO you should use PASSATO PROSSIMO after too.
Ex: Lui ha detto (PASSATO PROSSIMO) che ha comprato (PASSATO PROSSIMO) una nuova auto.
But not finish here: there are more verb forms... Good luck with the Italian verbs! ;)