I think you're correct, mostly. Debt is a type of liability, but not all liabilities are debt.
However - taxes "owed" are a liability, yet they aren't a source of funding.
The only definition that covers all liabilities as far as I know is "financial obligation towards another party".
taxes is actually an excellent one to debunk this: you “owe” all future taxes, yet they are not liabilities. a deferred tax is a liability because it represents a counterfactual funding: you would otherwise have had to take cash down or debt up to pay it.
“funding” doesn’t need to mean an investment contract. it can mean the financial equivalent of providing or receiving such a contract. accounts payable is a nice example too: that is your supplier giving you credit, which otherwise you would have needed to borrow to cover.
as I said elsewhere, consider accrued interest, goodwill impairment, and negative equity if you want to force the idea to its nonsense conclusions.
I am not saying the examples you give of certain liabilities as a form of funding are wrong - I agree with them.
But your reduction of ALL liabilities to funding is incomplete, as can be seen with taxes.
Taxes owed are a liability on a company's balance sheet and they do not represent any source of funding.
They do represent, like all other liabilities, a future financial obligation towards another entity, in this case the government.
This is what all liabilities have in common.
taxes only ever go on the balance sheet if they are deferred, in which case they have created a funding need. this is literally what ties the entire concept of a balance sheet and accruals accounting together.
EVERY liability represents the matching of funding to allocation. that it is an obligation to somebody is only ever a coincidence.
Your original note said "source of funding", not "source of need of funding", though.
