Hm, that's a good point. I forgot about the free travel within the EU. Still I recall that 5 or 6 years ago, there were checks at the Romanian-Hungarian border.
After doing some research, it seems that while Romania is in the EU since 2007, it, together with Bulgaria are not yet in the Schengen Area, so there should still be a border between Romania and Hungary.
https://en.wikipedia.org/wiki/Schengen_Area#Temporary_border...
But even if countries don't keep particularly __good__ records about persons passing their borders, I find it hard to believe that Romanian authorities used the video from a tweet to confirm Tate's presence in the country.
EDIT: Moreover, I've got the impression that the Tates are not the type of people to travel internationally by car. I imagined they flew in and out of Bucharest.
