I know that a lot of time has passed since your post but I also have the same problem using DropBox and GO. In my case I am using OS8 and FM GO 13x on my iPad Mini.
Have you found a way to resolve the issue? I have been going into Home on the iPad and manually deleting the previous file from both 'Recent' and 'Device' and this method is hit and miss. There must be a way to clear the cache.
Another bug (as in it bugs me) is that precious iPad memory is taken up by all of these old files from previous downloads. Is there any way to delete them other than manually?
I've found it's the dropbox app itself caching the copy, not filemaker go. We had a similar issue and the only users with issues were the ones that had the dropbox app installed. Users that were given the dropbox share link via email never had issues.
Unfortunately, there is no setting for the dropbox app to clear it's own cache on a regular basis AFAIK, we've only solved persistent issues by deleting and readding the dropbox app.
In FileMaker Go, if you want to delete files there IS a way to do it, basically by exporting a blank file (found set of zero records) of the same name to the get(documentspath) location. More details here:
Thanks for the information and Leo's link. I'll play with this awhile and see if it does what I want it to do.