I don't think the bank problem is really that big.
In the worst case, if the banks are shortly before a collaps, the european central bank together with the italian government will give them money and buy their garbage papers.
The ezb simply can not let it happen that a bank their goes bankrupt.
No matter what the treaties say.
So it will not have any big impact on bitcoin.
Your mixing three aspects here, but only give a rationale for one of them (#2):
1) The magnitude of the Italian banking problem,
2) the possibility of the ECB to refinance collapsing banks or buying junk bonds in case of a collapse,
3) the impact of an Italian banking collapse on Bitcoin
You indirectly assume that an uncontrolled (i.e. without ECB intervention) collapse of the Italian banks would have a significant effect on Bitcoin. However, what makes you think that the majority of the Italian / European people will first think of Bitcoin (and not gold, for example) if banks are collapsing?
The argument that certain changes in fiat valuation of Bitcoin were the result of real world events (Cyprus expropriation, Brexit) has been widely circulated. However no proof for these assumptions was ever given.
ya.ya.yo!