That said, it's possible, per that link, that Brussels bureaucrats could fudge and hope the above happens, or it's possible that the Commons, where a majority of current members allegedly were 'Remain' (if only for public consumption) could indeed do nothing, as discussed further here by Slate.
Each in turn.
Brussels, having the measure of the UK Independence Party, the long run-up to the referendum, and, for good measure, decades of British soccer hooligans traipsing across Europe,, probably is in no such mood.
Contra the 'no drawbridges' words of former London mayor and 'Leave' leader Boris Johnson, the EU is determined to have no shilly-shallying, judging by first, the comment by the foreign ministers of the original six members, urgings from leaders of member nations and now, the note to David Cameron, or hint, or push, that he can start the process on Tuesday. (Even if Angela Merkel is a bit more charitable.)
It's true the EU cannot force the ball to start rolling. However, it can clearly indicate from the start, in ever more forceful terms, that any halfway house associate membership is not up for negotiation.
As for the Commons doing nothing?
That first presupposes Theresa May winning the Conservative leadership vote over Boris Johnson, I think. It second presumes that Labour ousts Jeremy Corbyn after a party no-confidence vote against him passes and that his replacement is fully Remain. And, I do not think Hillary Benn (now sacked) was some eminence grisé behind Corbyn; his muffled mouth was his own choice — and votes of rural Labour in Sunderland were their own choice. And if the party really had serious concerns about Corbyn on this, the non-confidence vote should have been brought at the start of the campaign.
(That said, how a Labour-leaning area thought voting for a measure favored by the right wing of the Tories, and even further right, would help their plight, I don't know. Another sign that many British voters are at least as dumb as American ones.)
Let's say Johnson is tapped on the Conservative side as leader.
It seems clear that if a Johnson (I doubt Nigel Farage had this attitude) thought of playing a Leave vote as part of a renegotiated associate membership deluxe or similar, that's not in play across the Channel, per the note to Cameron link.
And if he tries to backtrack, when Brussels spells that out again?
Sidebar to the Scottish Nationalist Party — call for second referendums on independence all you want. The EU isn't likely to admit you. In a word, on why: Catalonia. (OTOH, a Merkel ally says Come on Down!)
And, as I said last week, the idea behind Brexit wasn't totally wrong. Whether Brussels listens is anybody's guess.