Refresh my memory. I know that we tell customers they cannot deposit receipts from their business into their personal accounts. Someone says it is OK, for example a check made payable to XYZ LLC and Jane Doe and jJne is trying to deposit the check to her personal account....is this a law or reg or that governs this practice???

This is a good start - http://www.bankersonline.com/operations/guru2006/gurus_op070306d.html
With a LLC and an individual, you're still dealing with 2 legal entities, so if there's any disagreement about the funds between them, the bank could be caught in the middle.