They don't cart it around airshows. The airshow where I flew on it was in Zhukovskiy in Moscow and it was there so the president could go and check it out the day before. It is permanently based there. And and I don't know the name for these sims, but it's one of those that you can train a pilot from scratch and the 1st flight on the real aircraft would be a commercial flight in the right seat.
Here's a video of it:
It's in Russian but I'm sure you can see it's not a fake sim. And if you understood Russian, then it basically says what I just said above.
I am not going to say how accurately it is currently modeling the environment as it hasn't been certified yet. So in that respect you may very well be correct - it might not be as accurate as the real thing.