This error for sure appears to be related to reading a database/collection/document which does not exist. I got the same exact error for a database that did exist but I input the name as lower case, this error appears to happen regardless of your partition key.
The best solution I could come up with for now is to wrap the 
var response = await client.ReadDocumentAsync(UriFactory.CreateDocumentUri(database, collection, "documentid"));
call in a try catch, not very elegant and I would much rather the response comes back with some more details but this is Microsoft for ya.
Something like the below should do the trick.
                Model myDoc = null;
                try
                {
                    var response = await client.ReadDocumentAsync(UriFactory.CreateDocumentUri(database, collection, document));
                    myDoc = (Model )(dynamic)response.Resource;
                }
                catch { }
                if (myDoc != null)
                {
                   //do your work here
                }
That is to get a better idea of the error then create the missing resource so you dont get the error anymore. 
A few resources I had to go through before coming to this conclusion:
https://github.com/DamianStanger/DocumentDbDemo
Azure DocumentDB Read Document Resource Not Found