Oh totally make sense. Thank you so much! Crystal clear.
For future reference, local modifiers will usually change something in the values shown above mods on the item, and usually make those values display in blue rather than white - because they're applying on the item and changing those properties on the item. So if you compare two weapons where one has a local damage modifier (including quality) and the other does not, you'll see the value near the top of the weapon for it's damage includes the effect of the local modifier. Anything which changes an item's base values that way is a local modifier.