Yes it would. This is the same guy who required the police to get search warrants before letting them into the house to search for clues in his wife's disappearance. Catching kidnappers need not come with the cooperation of the next of kin as it is the people of California who want the kidnappers apprehended.
Because we "think' something may be going on
You are not accurate in paraphrasing my second reason. His own words stating that he knew who did it hardly qualifies as a fishing expedition. The next of kin tells his secret girlfriend that he knows who is responsible for his wife's disappearance and you call that fishing? (And the police have it on tape...from Amber's willing phone tap)
As well they should. He has a legal right to document WHY they are in his home...