Do we take that as agreement the quote that was before the vote was intended to influence things and relates to the heading

Perhaps you need to read the article.
Under the Guardian's "Promise 1" It says "Brexit will be easy, and have no downsides".
The only quote given in that section which predates the referendum is from Michael Gove, and says: "The day after we vote to leave, we hold all the cards and we can choose the path we want"

Clearly it does not promise what the guardian claims is being promised, and any other quotes in that section were made after the vote had taken place.

What next? Gove states "two plus two is four", and the Guardian claims that that is a promise that it won't rain at all this July?
There should be some connection between their claims, and the quotes that they claim backs them up.