I'm pretty taken aback by the prospect of this definition of debt being "strict".

Debt is money borrowed from a lender and owed back at interest."

Do you think anyone on the street is going to disagree with that and call it too specific?
I think you'd be hard-pressed.

For instance, if you open a non-interest-bearing checking account the bank is obligated to pay you back.

This is actually just another reason why HBD is not debt. Thanks for reminding me. Depositing USD in a bank incurs a 1 to 1 debt. You deposit fiat and you are owed fiat. That is not comparable at all to our system with two completely different assets connected by 3.5 day price feeds and haircut limits.

HBD allows us to outsource some of our emissions and create value on its own merit. To assume that HBD is debt is to assume the network can't grow as fast as the inflation rate. Seeing as the inflation rate for HBD is less than like 3% of the network's total market cap this is quite obviously not a problem. The demand for HBD will almost certainly increase faster than the inflation rate and continue generating value seemingly out of thin air.

Someone reading this statement may say that HBD is not the same as DAI

Nice work

You point out yet another reason why neither of these assets are debt. They are both overcollateralized by 300% or more. In fact HBD is 1500% collateralized. Imagine trying to tell someone that the $100 they created from $300 worth of collateral is somehow money that doesn't exist that needs to be paid back later from some other source of income. The fact that DAI forces users to pay interest on their own money is absolutely mind blowing. It's a testament to how early in the game we are and how poorly the tech is understood.