IOW you are not paying with BTC, you are selling BTC for some fiat currency and using the proceeds to make the payment.

If I take my US debit card to Europe and buy things there, essentially the same thing happens.

But you are not paying the European merchant with USD.

Neither are you paying with USD even if your debit card directly debits your USD account. It's a proxy for paying with USD, just like a bitcoin debit account is a proxy for paying with bitcoin. That the conversion and account adjust ment happen in one currency or another does not mean that currency is directly involved, it is merely a convenient stand-in for the number reflecting your balance, an attribute of it.

People think that banks hold their money: they don't. The bank simply owes you your money but they don't hold it for you. What you get in return for your money is a statement from the bank what debt they owe you and a device to convert that debt into goods whenever you feel like it. That device is not the same as the underlying money, it is merely a proxy for your debt.

Which you'd find out about in a hurry if your bank ever went under and your card stopped to work.

Are there standard mag stripe/chip cards that draw from a BTC account and exchange into fiat at the time of purchase of a good?

All the cards I've seen when I looked into it a bit ago converted into fiat at the time of charging the card with BTC (ie, you send BTC, that got converted into fiat immediately (at pretty mediocre rates), and then you could use that fiat to purchase stuff or withdraw cash (at pretty mediocre rates, again)).