Which being the case, it’s probably best to ignore three red herrings that have sent Greek markets spinning today. One is little more than a rehash of old news, another is a seemingly garbled answer to a left-field question by Gavriel Sakellaridis, the spokesman of Prime Minister Alexis Tsipras, and the third (and most interesting) has been officially denied.

Markets sold off early on a report in the Financial Times, citing a letter in which Tsipras warned International Monetary Fund managing director Christine Lagarde that Greece couldn’t make a 775 million euro ($875 million) debt repayment to the IMF. This was both a) old news and b) just Athens crying ‘wolf’, as the payment was made anyway.

They got in even more of a tizzy when Sakellaridis, at a briefing, started denying plans for a levy on depositors at the banking sector (no-one really thought there were anyway, which made the denials raise eyebrows).

Later, markets reversed after a report in the newspaper To Vima that European Commission President Jean-Claude Juncker has offered at least one important concession to Tsipras as the two sides try to find a way to get Greece’s almost-defunct bailout back on track. The Commission has now denied it, but as we’re talking about Juncker, who candidly admitted to tactical lying earlier in the euro debt crisis, people shouldn’t feel obliged to take that denial at face value..

To Vima said Juncker proposed relaxing Greece’s primary budget target for this year to a surplus of 0.75% of gross domestic product from an original target of 3%. He also seemed willing to postpone until after the key summer tourist season a demand in the bailout for Greece to raise value added tax rates and end some exemptions.

Given that Greece has fallen back into recession as fears of an exit from the Eurozone have risen, the target of a 3% is dead in all but name anyway, so it costs the Commission little to acknowledge it.

But together with the other olive branch, it’s enough of a concession to maybe elicit a response from Athens. With goodwill and a little more flexibility, the two sides might yet agree a deal that would unlock €3.7 billion in Eurozone loans to Greece, giving it a fighting chance of making some big payments to the European Central Bank and IMF over the next couple of months, and thus avoiding a messy default with imponderable consequences.

What is clear is that Greece is running out of money, if anything, a little faster than most people thought. Sakellaridis told journalists today that the government had enough money to pay an estimated €2.5 billion in wages and pensions at the end of the month, but that anything after that will depend on some last-minute diplomacy.

Talks at a technical level are still ongoing in Brussels, and they will be able to provide fodder for Thursday, when Tsipras, Juncker and Germany’s Angela Merkel (but by no means all of the Eurozone) attend a meeting in Riga on the E.U.’s “Eastern Partnership.” But there can’t be any formal deal without the whole “Eurogroup”, the college of 19 Eurozone finance ministers. They aren’t scheduled to meet again till June 18, and there’s no emergency meeting in the works to suggest that a deal is close. And in any case, the Eurogroup and Juncker are far from seeing eye-to-eye with each other on what needs to be done: it’s not Juncker’s money at risk, after all.

Ultimately, default is too near for anyone to ignore distractions like today’s, but it’s still far enough off to allow rumors and denials to circulate freely without material consequences.

As Nick Kounis, an analyst at ABN Amro in London, puts it: “The official deadline of the current bailout extension is the end of June, but we have serious doubts about whether the country could wait that long for financial aid. Several payments to the IMF are due in June (total around €1.5bn). So we think around the end of this month the pressure to reach an agreement will really become acute.”

As we’ve written before, missing a payment to the IMF isn’t the end of the world, especially if a deal with the Eurozone is in touching distance by then. It would, however, make it impossible for the Fund to pay out its share of the remaining €7.2 billion in the 2012 bailout–a point implicit in the way Juncker’s leaked memo makes no mention of IMF money.

But there is virtually no margin of error left now. Bloomberg reported Monday that Greek banks are fast approaching the point where they have nothing left to pledge for the emergency ECB money they need to plug the holes left by deposit flight. Outflows will only pick up if there is more loose talk about Cyprus-style bail-ins. And publicly accusing ECB President Mario Draghi of being a coward, as Finance Minister Yanis Varoufakis did last week, is arguably not the the best way to keep the central bank on board.

Watch. This. Space.