According to the HP Quality Center Support team, this REST call problem is caused by a product defect.
HP was able to execute this REST call successfully on ALM 11 and ALM 11.52, but not on ALM 12. So my ticket was converted to a "known problem" and now I need to wait until HP releases a fix for that. The bad thing is, HP doesn't have any estimative about when it's going to happen.
This is really bad, we only upgraded our Quality Center from version 10 to 12 because of this REST functionality. We were integrating our HP ALM 12 with another product, via REST calls, and now this integration project is stuck because of this known problem. This is unbelievable!
If anybody needs to integrate Quality Center with another tool I'd recommend to use ALM 11 or 11.52, but not 12.