On our contribution form, we allow people to contribute "On Behalf of an Organization" however it's not required.
The problem is even when that box is left unchecked, they get to the confirmation page without error, but when they actually click to submit the form, it says that the organization fields are all required.
It looks like this person had a similar problem. https://forum.civicrm.org/index.php?topic=35137.0
Here's our form: http://rivertreesingers.org/support
If you test it, just check the mail a check option to go through, but it shouldn't let you complete.
If it seems like a bug, where should that be reported? I'm on CiviCRM 4.7.3 in a WordPress environment.