This is not about looting; it's about gear the Shadowrunner actually bought.
Is this a correct interpretation of ownership?
All legal, restricted, and forbidden devices capable of connecting to the matrix (all electronics other than RFID tags) have an owner. (Ownership is presumably tied to a SIN.)
When a fake SIN gets burned, everything that was "owned" by that SIN can be located by the authorities, just as if it had been stolen, when it's connected to the matrix. If you legally transfer ownership of anything at any time from a fake SIN that is later burned, authorities can track all those previous ownership transfers, find out what SIN(s) the items were transferred to, and thus compromise other SIN(s). If this is the case, you effectively can't legally transfer items. You must illegally transfer ownership or carry all items turned off once the ownership data is compromised.
Thanks!