Like in a jury case, reasonable doubt doesn’t mean “a small level of doubt is acceptable”. It means that “aliens made me do it” is not sufficient to counter evidence.
The best approach is to know your rights, remind them of them, then let them do what they are going to do.
Bad searches get solved in court, not at the time of the search. You may get lucky and have them back down if it's clear you know they have no right to search, but I wouldn't bet on it.