NEC ECC: Under the NEC what does "Access Date" mean

Unless there are either a number of access dates giving access to different parts of the building, your interpretation is correct.

However, there may be further constraints on access stated in the Works Information (NEC3) / Scope (NEC4), which you would need to comply with. If there are not, then the Project Manager need to issue an instruction changing/adding the constraints or instructing you to stop parts of the works. Both of these circumstances are a compensation event.