I think the wiki FAQ needs a section on "Why do I lose morale for submitting to inspection?" In it, I can point out how small that morale loss really is, but I'd like to have a lore reason for the morale loss. To my knowledge it is just because your bunk gets tossed while they look for anything they disagree with, but I'd want that nailed down before proceeding.
As you said, tossing of the bunks or roughed up by the enemy crew or the rank and file don't like the captain's decision. Crew on a ship have their own opinions about how things should be done, and the captain stilling the engines and letting another crew come on board feels like an invasion and the crew doesn't like it.