I find it very interesting that remainers on the one hand complain they were not given sufficient information prior to the referendum, and on the other complain that 'illegal' donations swung the vote,presumably by enabling too much information. 
Is there not a rather fundamental flaw in the argument somewhere?

Not in the slightest. The problem lies in your presumption it provided information.   However information and propaganda are quite different, whichever side is providing it.

As a general rule, all political advertising everywhere in the world is far more concerned with swaying opinion than providing information.