Without the current design, you cannot have a zero trust system.
Most efficient designs are of course possible, but decrease trust. SPV is an example.
Wow, it's really powerful statement and really questionable. I hope it comes with formal proof

Blockchain system can secure almost any underlying data structure (think of namecoin) and I don't see why it cannot be account ledger.
You snipped the relevant, quoted context for the response given.
The entire transaction history is required for a zero trust system.