I don't know about NEVER trusting your banks.....I wouldn't put all my life savings in them (maybe some), but some banks are really good about taking responsibility for fraud issues and such. Plus, I like the cashbacks I get back through my credit cards.
Most banks can be trusted and putting your life savings is safe because they have insurance with your deposits you will feel safe.
Putting your money with bitcoin is not safe in terms of value because you are not saving at all but you did the investing activity which makes you money at risk.