my scientific education means I work with facts, and theories that can proven/disproven
That's what you work with, but you should know about more than that. If you really weren't taught critical thinking, evaluating sources, assumptions, biasses, any of that stuff, then we haven't succeeded in science education.
How was I supposed to prove either way what would be the right decision when even the politicians who are getting paid for this don’t know their arses from their elbows?
You are supposed to be able to look beyond politicians, who have their own interests. That's why there was a referendum.
And I refuse to be held accountable for what anyone else did with their limited knowledge - On both sides of the argument.
You are just as accountable as anyone else. No more and no less. But not willing to take responsibility for making the decision.