Dave's take is actually backwards if you think about probability. Rerolling ones on a d20 is a 5% swing in your favor, but the dice gods in most tables I've played at punish the PLAYER who rolled it, not the table. We had a guy in our last campaign who argued the same thing for three sessions straight, and what finally settled it was him rolling three natural ones in a row during a boss fight. He wanted to reroll all of them, but nobody would let him, and honestly that moment became the funniest thing we still talk about. House rules are fine IF everyone agrees before the dice hit the table, but adopting one just because one guy is loud about it is how you end up with a table where everybody has a private rule that only helps them. You're not overthinking it, but you should bring it up at your next game and vote on it like adults instead of letting Dave's 3 AM philosophizing rewrite your group's history.

Ever tried swapping the battery yourself? I did it on mine a couple years back when the drive started acting up, took about an hour with a cheap kit from eBay and it bought me another 2,000 songs before the screen finally gave out.