Everything you say is true except for your second statement. If they have a warrant they have the right to look.
If the police have a warrant and are looking for storage devices and then use URL to find a USB sticky thingy in a jar in a box under your floor, then I would support them tagging that USB thingy as evidence and looking at what is on it. If it's your family vacation photos to Russia or even ordinary porn, then it can't be used as evidence against you. However if there is one image of child porn on it, then I hope they arrest you on the spot and you never get out.