This applies to simple xlsx version 0.6.4 from the website.
The xlsx-File I tried to read with the package had wrong permissions and was unreadable for the web server, so _unzip immediately returned with error set to "file not found".
Unfortunately, this is not noticed in __construct - so parse is called, which in turn realizes that _rels is not available, and overwrites the error message to "missing _rels". Since there are several posts about similar problems, I think with most of these actually something went wrong in _unzip - whatever goes wrong, the nice error message is simply overwritten.
I propose to check the return code of unzip in __construct (or somewhere else).