I don't know that I agree with the "much, much more" but no doubt the factors that you mention are important.I actually think the ability to impact the fiction is much, much more reliant on factors other than stats.
For example, proactive players have a much higher chance to impact the fiction because they engage with it more.
Players that have more robust mechanical options for changing the scope of play (say, the Teleport spell in 3.5 D&D) will have a better chance of impacting the fiction.
<snip>
Players that have abilities that match the campaign theme have a much larger chance of impacting the setting than those that don't.
I would have hoped the "everything else being equal" was fairly obviously implicit in what I said.I'm not saying that stats don't matter. But they're only one piece of a huge puzzle that makes up the list of factors that come into play when seeing which player gets to impact the fiction the most. And sure, you can say "all other things being equal, stat generation and distribution matters greatly." While that's theoretically true, that's not how things generally work in a practical sense; all other things aren't equal.
As to the extent to which other things are equal - well, as you know, I prefer an approach to PC build and GM techniques which helps ensure a tight nexus between PC capabilities and campaign theme. I like to play with pro-active players. And I prefer that all players have access to robust mechanical options. So I try to push the factors that you mention towards equality.
But even if they were not equal, that would not be an argument that rolling stats is fair, for my style of play (and as far as I can tell you weren't running such an argument). It would actuallly be an argument to let those playing mechanically less robust classes to have better stats, and to let less proactive players have letter stats. (And that is actually an approach that I have taken, in a slightly informal and ad hoc way, in past Rolemaster campaigns.)