Sorry, Google's permissions settings are simply not that granular. In their eyes, the choices are
- Can view
- Can comment [and view]
- Can edit [and comment and view]
and those choices can be offered to individual accounts by email address, to anyone with the link, or publicly on the web. Google is a huge company, but if their choices are causing a problem for you, they encourage users to choose Report a Problem from the Help menu, and explain it to them.
On a higher level though, if an account can edit a given document, then they can do whatever they want with it—overwrite its contents, change values, or; naturally, they can make their own copy, whether by copy-paste, File→Make a copy, or by download—so with a good faith hope that your situation gets resolved, I must say that I think you'll have to solve the problem with, say… conversations, rather than checkboxes. Good luck.