The Christmas Tree would represent the address to which the trailer was being sent and nothing else.
These things do not signify the parent unit, but are merely a "postal address" for want of a better / simpler explanation used by the Movement Control people at a particular point in time, to assist in their job of moving stuff around the world.
To simplify things even further, Diana, if you are allocated the number, "1234", and I want to send a trailer to you, I mark it "1234" and it gets to you. No one outsides those who allocate the numbers really have any inkling as to who 1234 is, so the movement is relatively secure from prying eyes, and the fact that it is me lending you my trailer, to outside eyes, is irrelevant and not mentioned, unless I put my mark on the trailer. What you do with it once you get it is besides the point.
Don't put too much importance on Christmas trees, as I have said earlier in another post, I have seen serving vehicles with three entirely different "trees" and numbers still visible on them.
Regards
Glen