It's possible they're using the term "debit card" to refer to the EFTPOS network. EFTPOS gives you the SAV and CHQ options to pull money straight out of a bank account.
Visa or Mastercard can pull money out of a bank account too, but they do it via the credit (CR) function. If it's a credit card, the funds are drawn from a credit facility you've negotiated with the card issuer. If it's a debit card, it uses the same logic but the credit facility only extends as far as the balance you have in your bank account.
In that respect, your Visa/MC branded debit card is functionally the same as a credit card.
Visa or Mastercard can pull money out of a bank account too, but they do it via the credit (CR) function. If it's a credit card, the funds are drawn from a credit facility you've negotiated with the card issuer. If it's a debit card, it uses the same logic but the credit facility only extends as far as the balance you have in your bank account.
In that respect, your Visa/MC branded debit card is functionally the same as a credit card.