SSRS ReportExecutionService and 401 Authorization Errors

I was calling the SSRS Web service from the same machine and suddenly started getting 401 Authorization Errors. I finally found the cause.

Previously, I had been accessing the webservice with "localhost" in the URL, but at some point it got changed to the machine name. That’s when it stopped working. Apparently, a windows security feature called the "Lookback Check" causes this.