Eurozone banks do not trust each other: block of the interbank market ?

On Thursday there was an unexpected surge in funding facility required by the banking system to the ECB. As I explained in the post "Monetary policy of the ECB and the quantitative easing ^ -1", the banks may require to central bank liquidity through the so-called "marginal lending facility", which are overnight operations, which serve to eliminate imbalances of liquidity for one day and are an alternative to trade in loans made directly between the banks (with the application of EONIA overnight rate, the lower the rate at which place the marginal lending facility).
Well, on Thursday there was a record request of 8.64 billion euros from banks to the ECB, when the daily average in November was 2.4 billion.
Along with this news, that for a large increase that has taken place simultaneously in the "Marginal deposits", ie the liquidity that banks deposit with the Central Bank, amounting to a record 314 billion euros (just think that the on 6th November 2008, following the bankruptcy of Lehman Brothers, the marginal deposits were about 297 billion euros).
Now, the rate at which the ECB lends money to banks overnight is fixed, as an instrument of monetary policy, at 2%, while the overnight rate among the banks was 0.736% at 1st December. Similarly, deposits with the Central Bank shall be remunerated at 0.50% lower.
So why the banking system prefers to borrow at higher rates and the banks with excess money be paid with lower rates?
Simple, there is an obvious reluctance of banks to lend funds to each other, indicating a huge lack of trust. And certainly, if they do not trust each other ...
Such block in the interbank market certainly doesn't inject liquidity in the system of private and businesses; in other words, the banks deposit with the Central Bank and don't do credit.
But then, as you can talk about economic recovery, or rather slight recession, if individuals are unable to obtain money to allocate funds for consumption and business investment? Rhetorical question.
At this point neither the QE could be a solution, if the banking system doesn't return the liquidity obtained in the economic system.