Let me begin by saying stuff like what you describe is a reason people go to recognized shows with recognized judges and a mandated adherence to the rules so that what you describe doesn’t happen. And at recognized shows the procedure for tie breaking is as follows. If the total points are equal, the Collectives at the bottom are added up separately. The higher overall Collective score breaks the tie. If the Collectives on both tests add up to the same (whether one is straight sixes and the other is eights and fours), then the tests remain tied, and two ribbons are given out for that placing whether it’s for first or sixth.
Now the same thing is supposed to happen at schooling shows, but there’s no mechanism to ensure that it does. Long ago there was a more elaborate tie breaking procedure which involved taking the two tests back to the judge and letting us simply choose the one we preferred (and we got to pick our own criteria). That is no more, but occasionally a schooling show will still do it that way–particularly if they don’t have extra sets of ribbons to give out.
There is one other possibility (giving them the benefit of the doubt). That is that the judge did not go back and change the test after the fact (which in “real life” is very rare) but changed her mind as she was judging. Then the scribe is supposed to put a line through the original mark, put the new score beside it, and have the judge initial the change. This is normal and happens to me a handful of times a show day. I give the number but something at the end of the movement happens to make me change my mind. No big deal. It is possible that the scorer didn’t recognize this and tallied the original number. Then the checker came along and said, “Hey, oops, you’ve screwed up,” and made the alteration to the final placing on the test. Not real likely but possible.
Generally, dressage judging is based on “What I see is what you get” and adjusting scores so someone wins and someone else doesn’t isn’t part of the game. By the way, in the deep, dark history of dressage showing, this was less the case. 30 or 40 years ago many older judges would “hold” tests. When the runner came to take them to the scorer, the judge wouldn’t relinquish them. He’d keep a running tally of the scores he was giving (and therefore, the projected placings) and jimmy them up and down to get the horses in the order he preferred. Even then, this practice was frowned upon. Now it’s almost nonexistent.