Instead of "borrowed" you could say "owed" as you state. The basic idea is it represents money you have that you're on the hook for. Could be deferred revenue, accounts payable, bank debt, etc. I say "borrowed" because that's a concrete term that maps to a transaction with which most people are familiar.
I'd also argue that you can work through even the most complicated accounting transaction and build the most complex financial statements by repeatedly asking the questions I've outlined in the above framework. Accounting was meant to be simple and accessible for the layman, but for some reason every Accounting 101 class teaches things like "debit means left and credit means right," which causes most people to throw up their hands and just rely on bookkeepers and accountants for all things money related.
e.g. deferred revenue is a liability and although close, it is technically not really money that is borrowed. (It reflects services/goods owed)