Our MPs and MEPs are our legal representatives. We entrust them with the power to make our laws.
So if our legal representatives lie to us about our legal position, that's on them.
1) That the issue is simple enough for a two-way choice
Hence why Brexiters are now fighting over what sort of Brexit they want and some say simplistic fallacies like "Out means Out"
2) That neither option is catastrophic.
(In fact there are different isotopes for each chemical and some go boom fast)