Private upload overwrites file if file with same name is uploaded

I am encountering the following issue with the private-upload-module:

If I upload a file with exactly the same name of a file I uploaded previously the file first uploaded is overwritten:
1. I upload the file example.doc private in node#3
2. everything is fine
3. I upload file example.doc private in node#6
4. everything seems fine, but the file in step 1 is actually overwritten
This is confirmed by the report in 'Private Uploed Settings' it says:
There are '1' files in the private folder, and the DB thinks there are '2' private files
5 if I delete the file in node#6. The file is deleted.
6 if I try to download the file in node#3 I get a 'Page not found'

I was wandering if the problem was caused by the file-upload-module or by the private-upload-module. So I did the same steps but unmarked 'private' when uploading. This went fine because the file is automatically renamed:
The first file is named:
example.doc
The second file is named:
example_0.doc

Is there a way to let the private-upload-module do the same or at least give a warning before overwriting a file?