I don't dispute that Trump at one point said "Muslim ban". Giuliani appears to indicate that Trump knew this was illegal in the form that it was literally said it on the campaign trail and that Trump called him up and asked him to figure out how to implement what was meant, not necessarily what was literally said, in a legal fashion -- "seriously, but not literally".
>It is clear that in this executive order, the intent and desire (Muslim ban) is imagined, then the subterfuge (the focus on law) applied, contradicting your original point
No, it doesn't contradict my original point at all. It is clear that Trump meant that he wanted to exclude terrorists, not Muslims. If the goal was to exclude as many Muslims as possible, they did a terrible job, because they completely missed the countries with the 5 biggest Muslim populations. The raw populations of the banned countries add up to about 140 million; even if we assume 100% of those people are Muslim, which they aren't, that still leaves more than 90% of the world's 1.6 billion Muslims potentially eligible for entrance to the United States. And the whole thing expires in 90 days. Not a very effective "Muslim ban".
This goes back to the same thing as the campaign. Seriously, but not literally. Trump said Muslim ban on the campaign trail, that is not in dispute. The issue now is whether he really meant a literal ban on Muslims, or whether he just meant a ban on the bad guys that are blowing us up.
Based on his EO, it appears that he meant the latter, but of course there will be people who refuse to let go of their narrative and assume the former because it makes it easier to justify their outrage.