while the bonds are sort of like debt, unlike debt, the bond company could simply take their money out and invest it somewhere else. Where as, what we think of as debt, the bank can't just take your debt and invest it somewhere else if it thinks it can get a higher return for it somewhere else.
It's just like saying schwabb or scottrade or a bank has a "debt" to each customer that puts money in it. Sort of true, but not really what you would consider debt because it doesn't act quite the same.
That is why it is called an asset management company. All it owes is the promise of a return, not necessarily the principle itself like true debt (unless it "bought" the bonds and has a loan out).