Evidence millions of years out of date wouldn't stand up in court if the timescales on which the system changed were much less than a million years. For most of the things we see in our everyday lives, this is definitely the case.
Suppose I present to a judge that, ten years ago, the defendant had a cole sore on his lip. Then, last year, a witness saw a person with a cole sore robbing a local Wal-Mart. Does my contention that the defendant had a cole sore ten years ago count as reasonable evidence against him? Of course not, we know that cole sores appear and disappear on scales much shorter than that. However, if I can generate a witness who says that the defendant had a cole sore just hours before
the robbery, then it would be reasonable to think that he had one during the time of the robbery, no?
Back to the universe. To address your concern, you have to understand the energetic and dynamical scales of the problem. We can fairly reliably say that the universe has been expanding for something like ten billion years and we have models that describe how we think it has done so. Now, although we can't say this for sure within the past million or so years, we can say that the physical
changes in the universe that are required to halt the expansion within the past million years are so extreme that they're rendered utterly implausible from the physical point of view. To my knowledge, there are no mainstream theories that would suggest such a serious change. Even further, the fact that we observed expansion for about ten billion years prior would make it awfully strange if the universe suddenly stopped expanding within the very recent past. That would put humans in a very special place in time, a sort of hubris that has proven to be wrong in nearly every circumstance that it has been previously suggested.
Just as cole sores don't disappear within hours, the universe doesn't change from apparent accelerated expansion to contraction (or stationarity) within a million years. It's just not plausible.