Did the genuine signatories actually read it?
I doubt it, they're just bitter at the fact that the Remain camp lost. That more people voted "leave" than for any single cause in British history doesn't matter: Democracy has delivered the incorrect answer, so democracy is wrong. And the solution is to change the rules. Interesting to see the pickle the parliamentary Labour party is in, after an improved (that is, more open) democratic process to elect the leader also produced the wrong result, and the establishment MPs are using the Brexit vote to try and chuck out the leader who had the overwhelming support of party activists.
That's why you see some of the Remainers demanding ex-post rule changes, that the whole thing be re-run, that Parliament should ignore it. Any outcome is better than submitting to the democratic view of the population. There's some commentard further up this thread berating "the sheeple" for voting Leave, and that shows the same contempt for the population. After months of fear mongering by the government, by the official voice of Labour, Liberal and assorted nationalist parties, by the BoE, by the EU themselves, apparently we're still not to be trusted to come to a correct decision.
I think there is an amicable outcome possible. Give the Scots independence. Don't risk another referendum, since the SNP calculations for the Scottish economy won't fly at current oil prices. Then, the Scots can join the EU, all the south-of-the-border Remainers can claim asylum in Scotland, and then live out their days in a single party socialist state, where they can have both democracy AND a never ending socialist government within the EU. The Scots can get rid of other people's nuclear deterrents, England can scrap the Barnett formula.
What's not to like? The only thing I'd miss if Scotland went is the Union Jack.