The problem estimating financial company default probabilities is that as long as an asset is performing--ie, not past due--they all look the same. A bank could have a bunch of mortgages where their borrowers had FICO score above 600, and 20% equity in their houses (ie, good loans), or they could have mortages on borrowers with no money down, FICO scores below 500, and negative amortization loans. You have no way of knowing based on the data they present in standard financials.
But a firm like Bear should have a complete top-down risk report that aggregates their risks in a meaningful way, and so things like FICO scores, or subordination of the debt, should be available. If they can't pull this together, either they are hiding something, don't have this information, or think they have valuable trade secrets within their balance sheet. I truly doubt their firm's value is significantly generated by something as top-down as their risk exposures, but eventually they might have to to save their existence, and if they can't produce a concise summary, they should fold because this is a dramatic dereliction of duty.
I'm amazed how some big firms are really quite stupid, like when American Express lost over $1B in 2001 on junk debt. The president at that time, Kenneth Chenault, expressed shock at the losses, though the returns on the debt of 13% necessarily implied a large default rate risk.
I have no sympathy for Bear, because they should have the ability to convince people they do not have risk, and if they can't present information to that end, they are inept.
update (3/17): I think this is a case of a liquidity event forcing bankruptcy. Bear would have made it if they could mark assets at book rather than market value, but the market value made them insolvent, and if they sold for $2, they knew they were insolvent if one looked at mark to market. Thus, a great value add for JP Morgan. It's no different than if you all the sudden made Ford or GM recognize the size of their off-balance sheet liabilities (unfunded pension and health care), they would need a white knight.