You have to apply Extended Reader Rights to the saved PDF from LiveCycle Designer or use a LiveCycle ES server to apply the Extended Reader Rights to the PDF.
If a user uses the Apple Macintosh Preview application to complete the form, then you may have data but you will not see it because Preview causes a fixable/repairable issue with the PDF fields.
There are a few comments to address. 1. You might get more info about settings with Designer forms in the LiveCycle forum, though many here use them too. 2. Filling out a form should not require extending rights to Reader. The extended rights are only so that the form can be saved, and that a submission of the entire form (not just data) can be submitted (requires the form to be saved). Extended rights also offer other features, but these are the ones relevant to forms.
The comment about the MAC does not seem to be related to your question, though it is useful information. There should be no reason that the form should be restricting completion unless something else has changed in the form and saved. Please indicate the exact steps used to activate Reader Rights and all steps after that to where the message comes. It may seem to clear to you, but is not that clear on this end. Basically you want to take folks through the steps you have done so they can try to repeat it. Also indicate what versions of the programs you are using, not just AA9, but AA9.3.1 for instance, and also the OSs you are working on.