Also find this confusing, but this thing is a bit tricky.
I don't know why, but RNA path for nodes isn't full when copying. For me, it is not working without adding
node_tree. before copied data path.
Add another variable, which defines object data (Loc/Rot/Scale). You don't need to add variable to expression, just make sure it is in the list. And better use neutral object or Empty to avoid cycle dependecy
More complicated way
Delete current driver and add it via Outliner. In Outliner switch menu to Data Block and find object that is using this material, then hit plus sign to expand tree and find material slots -> desired material -> material nodetree -> finally node you want to drive.
In other words, you should go through the whole data tree - from object to desired node's value.
Once you find line with value (for this specific case - Default Value), select it and click Edit in the header -> Add Driver
This is very brief explanation. For more info on Outliner method, watch this tutorial vid (from 19 minute).