Something does not sound right. Apparently the door knob was off since it was mentioned one needed a screwdriver to open the closet door. The four year old could stick his fingers/hand in the empty hole to pull the door shut once they were in the closet if they were playing.
However, that raises two questions for me. Living in the south in a house, my closets do not have door knobs on the inside of closets. So the child would not have the ability to pull the door shut as mentioned above. In fact, you would have to put your fingers under the door to pull the door shut. Also, closets in the last 40-50 years don't close by a turning door knob. I am not familiar with trailers.
The second question is would officers/searchers be carrying a screw driver to open the door? Or would they take the time to open the door in that manner? It may be that if no noise was heard inside the closet, the officer went onto the next spot thinking it is difficult for three little ones to be quiet if they were in there.
The four year old girl should be a wealth of information. IF an adult was involved in this, the children may have been threatened to not say a word. However, IF the person checking the closet failed to open it upon discovering it locked, and all quiet, do you think he is going to admit it? Hmmm . . .