Do we KNOW absolutely that Anna sent an email to him to get the stuff out of the house? I don't remember that at all.
from Shelley testimony: Shelley told the Enquirer that Anna gave him instructions to "take my computer and stop it from getting in the wrong hands" if she suddenly died. She seemed convinced something would happen to her".
(it's my speculation that, armed with those emails), he managed to convince the Bahama magistrate to allow him to enter the house, with police escort, and was getting these items when Polit Pol's 'wife' arrived on the scene, and was jumping up and down whining he had to wait (half an hour?) to get into the house. (DL had already been removed from the house at that point)