Leave take slender lead in final Opinium poll

I'm sure we'll have more polls tonight (Referendum Eve is very much like Christmas Eve, as veterans of the indyref will recall), but we've already had two so far today - and the news is mixed.  Leave will be delighted to take a 1% lead with Opinium, who in recent weeks have become one of the most Remain-friendly online firms after introducing methodological changes that essentially made their weighted sample more like a typical telephone sample.  But Survey Monkey show a small swing in the opposite direction, which leaves open the obvious possibility that nothing much has changed, and that any apparent shifts in either poll are just caused by normal sampling variation.  Both polls show a statistical tie - ie. even if the methodology is bang on accurate, it's not possible to say which side is in the lead due to the standard margin of error.  (I gather Opinium may have used a larger sample than usual, but even enormous samples have a margin of error.)

Should the United Kingdom remain a member of the European Union or leave the European Union?

Opinium :

Remain 44% (n/c)
Leave 45% (+1)

Survey Monkey :

Remain: 50% (+2)
Leave: 47% (-2)

I've just received the Survey Monkey press release by email, in which they describe the small reported shift to Remain as "decisive".  I must say that's a bizarre summary, and not just because Opinium have directly contradicted their findings.  Even with a sample size of 4000, it's absurdly bold to suggest that a 2% swing in a stand-alone poll is necessarily significant, or indeed that a 3% gap means that you've definitely got the correct side in the lead.  I suspect that Survey Monkey, just like BMG a few days ago, may be overstating their sense of certainty in the hope of gaining bragging rights for years to come if they just happen to be right.