turning one AP over when leaving US???

My attorney shocked me by saying

"If you travel using your Advance Parole, you will need to present a copy on your way out of the country, as well as on your way back into the country."

I have never heard about having to present AP when leaving the country. Does anybody know this??? Also, do I need anything else apart from AP and passport when returning back, like I-485 receipts, I-797 and etc?

Thank you!!!