I've just ended up querying this with them, and after a vague and contradictory first reply, they've now come back with:
I want to clarify that on your Platinum Charge Card you are required to make a full payment by the due date (14th days from the statement generation date) to avoid incurring a late payment fee. The 30 days time frame is in reference to the account going past due which will impact your credit history.
Not sure if this is what the T&Cs actually say... But it does seem to be a moderately consistent take on it.