<<I almost feel it's Google's cache that needs refreshing...>> Nice. For another take on that issue see [*] where someone had had enough of the advice to clear cache and cookies. Meanwhile we have the issue of the document that won't go away. One possible solution or work-around was posted on the GDocs forum here . It has also made its way into the GDrive known issues page  under "Google Drive on the web". The work-around is not always successful and several variants have been posted in attempts either to explain it more precisely or just to make it work. I think that the key variants are collected here as it stands today.
For GDocs following :
1. Select the collection in question.
2. Right-click or use the More menu to choose Organize.
3. Uncheck the box next to My Collections and click Apply.
4. You can now find it under All Items and delete it from there.
For GDrive the instructions in the Help page :
1. Select the items you want to remove by checking the boxes next to them.
2. Click More at the top of the page and select the "Unsubscribe."
3. Make sure the items you want to remove are still selected and click the folder icon (next to the trash icon).
4. Hold Ctrl (PC) or command ⌘ (Mac) and deselect all the folders with a check.
5. Click Apply changes.
For GDrive following Google's Ine under , a slight modification of the Help page instructions:
1. Select the items by checking the boxes next to them.
2. Click the trash icon at the top of the page.
3. Unsubscribe if it asks you to.
4. Go to All Items in the left navigation.
5. Locate the files and select them again.
6. Click the folder icon (next to the trash icon).
7. Hold Ctrl (PC) or command ⌘ (Mac) and deselect all the folders with a check.