Dispatchers and Handling agents do not have the authority to prevent a flight departing without the correct documentation. If the capt says he is going - then he is going, full stop.
However, the dispatcher can report the incident to his seniors and/or airlines ops/station manager.
Also, in my experience when a capt claims the DOW/DOI is incorrect, it is normally because the capt hasn't received his company's latest sheet of weights.
Finally, it is the policy of one low cost airlline to file an ASR when an incorrect loadsheet is presented to the capt.