https://www.fdic.gov/deposit/deposits/
Ownership category is just something like single, joint, retirement, etc. If you have more than $250,000 spread across multiple accounts but with the same account holder and ownership category, the excess is not covered.
Let's also make a note that people with $250k+ in cash savings are a tiny group that should have no really bearing on whether cash is trustworthy.
I think you still trust those services with your money in the same manner you trust classic banks - no real difference here, both can be used just for transfers and not keeping anything with them. Except for with banks it's really tiresome and inconvenient to load on demand and with Bitcoin it's nearly a one-tap experience.