The difficulty in all this is multifold. First, cash saving is essentially a negative act. In times of low inflation it is a safe act and, with deposit guarantees, broadly secure but it yields next to nothing and, as importantly, does nothing for the economy. Saving in cash effectively takes money out of active use. It is a loan to a bank that then forms part of its capital (it no longer remains your money: it does belong to the bank once deposited and all you own is a loan recorded in a bank statement) but what we now know is that banks do not then lend this money on: all the loans they create are made out of new money created for the purpose. They do not therefore, effectively, need deposits to make loans.
And given that banks runs do exist therefore this explanation must be incorrect.