I have a customer wanting me to drywall the basement ceiling which has junction boxes... I can not drywall over junction boxes correct? And should recommend she has a drop ceiling put in?
You are correct, the junction boxes must remain accessible. The NEC 314.29 prohibits covering up boxes such that you'd need to remove "part of the building" to access the wires inside. The drywall is considered "part of the building."
You can move or extend them so the boxes are flush with the drywall when you're finished, so you can access the wiring by removing the cover.
With a drop ceiling, opening a ceiling tile for access is not considered "removing" part of the building, so you can have junction boxes above the drop ceiling.
314.29 Boxes, Conduit Bodies, and Handhole Enclosures to Be Accessible.
Boxes, conduit bodies, and handhole enclosures shall be installed so that the wiring contained in them can be rendered accessible without removing any part of the building or, in underground circuits, without excavating sidewalks, paving, earth, or other substance that is to be used to establish the finished grade