I’m fairly sure that measuring departure and arrival time with a light beam over a short distance of only 3 feet is plenty of room for error. Like I said, how can something arrive before it leaves?
Who says that it did? And why couldn't it?
Step back and look at what you're saying: essentially, you're assuming that time is unidirectional.
It used to be that time was assumed to be unidirectional and that it changes at a constant rate. Einstein's breakthrough came when he challenged the assumptions about time -- and as a result, relativity dispensed with the idea that time passes at a constant rate.
Now: what if space-time is somehow different from what you're assuming it to be? It might be "impossible" according to your assumptions, but what if your assumptions are wrong?
I have no idea whether these guys are mistaken or not. I'm just not ready to call "impossible."
Like I said, how can something arrive before it leaves?
Consider your relatives. They arrive and you wish they left before they came.