Looking into this further, it looks like there’s a consistent pattern where all the rules I can’t edit are ones that have a “Slack - Send channel message” component in the “Do this” section.
I wonder if this is something for the Asana BUTs. Asana, show me your BUTs 🍑 - #46 by Phil_Seeman
B3.7 You can edit a rule that someone else created (provided the box is unchecked for “Only you can edit this rule”), BUT not if one of the “do this” parameters is to push a message to Slack.
I’ve solved this for now by just pausing my teammate’s rule and building an identical rule with the extra parameter I needed, but just wanted to share in case it was helpful to anyone else.