Spec Editor role is sufficient. you also need to have a UOM Category and Base UOM selected.
Looks like this was a bug. Thanks for the follow-up though!
There are a few situations where you won't be able to edit UOMs defined in the UOM conversion grid.
1. In general, once a UOM is active you can't edit it without the [AVAILABLE_UOM_ADMIN] role.
1. Regardless of role, once a UOM inside the UOM conversion grid is used you shouldn't be able to edit it. For example, if "Bag" is already used in a formulation you won't be able to change or delete the "Bag" definition