On several occasions, The Coast Guard has request permission to come aboard, as a Commical fishermen, they are always welcome*, part of their duty is doing safety checks, and inspections . Some of these can be done dock side , others have been do underway.While actively fishing, the most cases the Coast Guard will hold off till your vessel is in a position to take on boarders. As captain the safety of the vessel and crew are your first obligations , if at the time you feel that a boarding would place the vessel or crew in danger, you have the right to refuse, till it becomes safer for all concern.
The Coast Guard are there to protect and serve the boating public! They are part of Homeland Security which allows them a great deal of latitude in their operations.
When you are in trouble out at sea, they are the ones that are risking their lives to save yours!!!!