His recommendation is based on the USA consumer protection laws so it may or may not apply in other countries.
For credit cards, US law limits your personal liability to $50 (typically $0). "Under the FCBA, your liability for unauthorized use of your credit card tops out at $50. However, if you report the loss before your credit card is used, the FCBA says you are not responsible for any charges you didn’t authorize. If your credit card number is stolen, but not the card, you are not liable for unauthorized use."[1]
If you contest a charge, you are NOT required to pay that amount until the matter is resolved. Resolving it typically takes two or more months, but it isn't your problem and doesn't affect your life during this period. If it is resolved in your favor, dealing with the loss/recovery/reversal is not your problem, it is like it never happened (for you). The bar you need to achieve to show a charge was fraudulent is pretty low - typically a phone call to challenge the charge and a followup letter with a statement and any documentation available (as simple as stating you did not order/receive the goods shown or the goods were damaged).
Debit cards typically have limits to liability, but the stolen money is not restored until the matter is resolved. It typically is a LOT more work and can be several months to get the card issuer to make you whole again. Also, with a debit card, the theoretical limit of what the thieves can take is ALL the money in your bank account (and more with overdrafts). The bills don't stop while you are unwinding the mess and your money is unavailable... You can end up in a big hole; restoration of original funds that were stolen does not make you whole because of the "knock-on" charges and losses while your money was unavailable.
[1] https://www.consumer.ftc.gov/articles/0213-lost-or-stolen-cr...