Read the fine print (it's not provided at that link, that link says "Certain limitations apply. See deposit account agreement.") They literally give themselves an out if you have given your card number "to someone else". It's mighty hard to use a card without giving your number to someone else, so the protection policy could be interpreted to be utterly meaningless and it will be up to an arbitrator what "or ... someone else" means if you have a disagreement about this with your bank.

Debit cards do not have "a reputation" for having less protection in America. Debit cards do have less protection in America. With a credit card, you can lose $50. With a debit card, you can lose all of the money in your account and in all accounts linked to that account.

Chase has a policy of advertising zero-liability for debit cards. The US government has a federal law requiring $0 to $50 liability for credit cards ($50 if you lost the physical card and didn't report it before it's used, $0 otherwise). The US government has a federal law requiring tiered liability for debit cards depending on how fast you report a theft and providing no protection after 60 days. [1]

Meanwhile, bank policies may appear to offer better than federal law requires for debit cards, but in practice the fine print can ruin you, and it's up to the bank whether you get protected under their policy since it's not federal law, and at best you get arbitration to settle a dispute not a court.

See, for example, the exceptions Chase gives themselves in their 'zero liability' [2] & [3]:

"If your Card is lost or stolen, or your Card number is used without your authorization, if you notify us promptly, you are not liable for any unauthorized transactions, including transactions made at merchants, over the telephone, at ATMs, or on the Internet.
However, these special provisions do not apply where you were grossly negligent or fraudulent in the handling of your account or Card, where you have given someone else your Card, Card number, or PIN, or where you delay reporting unauthorized transactions for more than 60 days."

"You must provide us with all information we need to investigate the alleged error or item. You must also file any police reports and provide any supporting affidavits and testimony we reasonably request.
If
you do not comply with the requirements above, we are not required to reimburse you for any claimed loss, and you cannot bring any legal claim against us in any way related to the item or errors.

"You must notify us in writing within 30 days after we mail a statement or otherwise make a statement available (for example, paperless statements) if . . . An item that you did not authorize or that is altered is listed on the statement ... You must provide us with all information we need to investigate the alleged error or item. You must also file any police reports and provide any supporting affidavits and testimony we reasonably request.
If you do not comply with the requirements above, we are not required to reimburse you for any claimed loss, and you cannot bring any legal claim against us in any way related to the item or errors."

[1] http://www.consumer.ftc.gov/articles/0213-lost-or-stolen-cre...

[2] https://www.chase.com/online/services/document/deposit_accou...

[3] https://www.chase.com/online/private_client/document/supplem...