You may be severely frustrated setting up OneOrZero Trouble Ticket System. The demo on their site works perfectly and yet the local setup doesn't allow reporters to create task. The solution is simple:

Change "User Group Rights Control User Field Values" setting to Off in OneOrZero settings. This simple tip can save your life, remember it.

Update: On a fresh installation with a new version I found that this option was set to off. So either I had set it to on by mistake or it was an error with a previous version which has hence been rectified, I am not sure.