Disclaimer: I only skimmed this solution.

However, it looks like you don't/can't address all of the counterpart's liabilities. So salaries, tax dues, rents, loans, and other obligations denominated in fiat currency don't appear in the calculations. But any of these can destroy a counterparty as surely as insufficient reserves. Crucially, depositors don't really care where the risk is, they care that there is some external entity (like the SIPC or FDIC) that can insure that risk.

You are right, those other factors cannot be accounted for with this approach, it only proves that the business is not running with fractional reserves.