FWIW, the leaflets were part of the remain campaign. They don't claim that leaving the EU means leaving SM/CU; just warn about not having guaranteed access and, as @<a href="https://www.mmo-champion.com/member.php?u=630633" target="_blank">Pann</a> mentions, that staying in SM while outside EU would mean following rules. So the leaflet doesn't rule out the EEA.
Some leave campaigners were very explicit about it meaning leaving the SM.
Some other leave campaigners claimed that they didn't have to leave the SM. This was brought to light very early by Open Britain (
video here).
I have no idea why one would be so adamant as to claim with certainty that there is a mandate to leave the SM. To me, the leave campaign was noise without a clear path; packed with unlikely promises and dubious claims. To me, that's not what a mandate looks like; leaving the SM is the path of choice for the current government, that's all.