Sounds like the vacuum pump which provides suction for the lavatories on the ground was unserviceable. The 16,000ft figure is from the Airbus MEL (minimum equipment list) instructions for dispatching with the pump unserviceable, as an estimate of when the differential between the cabin and outside air pressure is sufficient to provide suction to the system again.

Had this a fair few times as a pilot on A320s, we normally kept the seatbelt signs on and lavatory doors locked until they were usable again.