It doesn’t surprise me that the internal coverage/sentiment was as diametrically opposite the external as possible.
True, none of the stay advocates was as charismatic as Nigel Farage, whom I love, but not all do. OK, so that’s one guy, and he’s a superman as far as I am concerned, having fought against the EU for 25 years. But the “stay” proposition was paraded (here) as an economic disaster for each and every stratum of society, from the farmer, to the entrepreneur, to the financial elite, to the clerical worker.
Truly, the lesson is how incredibly distorted media-driven perceptions can be, and are. I don’t think too many Americans thought the exit would be approved. I don’t think too many Americans thought DJT would be elected, whether they voted for him or not.
I think you would be surprised how low Farage's profile was in the UK during the referendum campaign (it was much higher elsewhere, especially in the US). The are several reasons why, I suspect, the campaign managers wanted him kept out of the limelight. Firstly, if 'leave' was to win it would be necessary to win over many middle-of-the-road 'don't know' voters, who tend to see Farage as an extremist and for whom he would be a turn-off if he were too prominent. Secondly, the British media - even the media most hostile to the EU, such as the Mail - have always tended to see Farage as a slightly comical figure, not a serious politician. They have tended to take more seriously traditional Europhobe Tories such as Redwood and Duncan Smith. Finally, there is Farage's identification with UKIP, which consistently failed at elections because of incoherent policies (except on its single defining issue), poor candidates and internal feuds.
For all the reasons it was probably felt that Farage would do the campaign more harm than good with the unconvinced electorate.