To Rotor bike's excellent and definitive citation, I'll add-
"§135.213 Weather reports and forecasts.
(a) Whenever a person operating an aircraft under this part is required to use a weather report or forecast, that person shall use that of the U.S. National Weather Service, a source approved by the U.S. National Weather Service, or a source approved by the Administrator. However, for operations under VFR, the pilot in command may, if such a report is not available, use weather information based on that pilot's own observations or on those of other persons competent to supply appropriate observations..."
...You can't observe what you can't see. In this case you have no way of knowing you're maintaining required VFR minimum visibility.
If you're working for an operator who micromanages and second guesses your judgement, I'd start shopping a new position.