Anna is absolutely right. The process before you get to a proof of debt is set out by NAB below but more than likely after you go through those steps you will be left with lodging a proof of debt (PoD)
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Some banks also specifically exclude claims when a business goes into external administration probably because the administrator (if a liquidator) has the right to refuse to honour any further obligations after their appointment.
Don't forget that this is not an Australian company - so the process may be a little different. In any event, the extent of the return, and timeframe are likely to be of little use.
Banks excluding or attempting to exclude claims are doing so because they may be liable. The ability of an administrator or liquidator to refuse to honour obligations is irrelevant here.
There are multiple parties involved, all with a variety of rights against each other. Ignoring the possibility for any given party to wear multiple hats, and ignoring additional intermediaries, in a credit card transaction there are likely to be 5 parties involved.
1. The cardholder. They have a relationship with the institution which issued the card, whereby they are liable to make payments to that institution for items charged to the card. They also have a relationship with the merchant, who provides goods or services to the cardholder, in exchange for the ability to collect payment from the financial institution which provides their merchant facilities (the acquiring institution).
2. The card issuing institution. Has a relationship with the cardholder, who has an obligation to make payments for transactions charged to the card. Has a relationship with a card scheme provider (e.g. Visa, MasterCard, American Express). which allows for them to issue cards branded with the scheme. The card issuing institution is liable to the scheme to make payment for transactions authorised on cards issued by it, and has rights regarding chargebacks etc., governed by the scheme rules. The card issuing institution may (and probably does not) have any relationship with the merchant acquiring institution, or with the merchant.
3. The card scheme provider. Administers the scheme according to the rules. Has relationships with the card issuing institutions, and the merchant acquiring institutions, with rights to and obligations to make and demand payments. May have no relationship with the card holder or the merchant.
4. The merchant acquiring institution. Has a relationship with the merchant, whereby they offer a facility which allows the merchant to make charges to cards, and they make payments to the merchant (in return for fees). Also has relationship with the card scheme provider, which allows the merchant acquiring institution to pass the charges on, and collect payment from the scheme provider. The merchant acquiring institution may not have any relationship with the card issuing institution, or the cardholder.
5. The merchant. Has a relationship with the cardholder, whereby they charge the card in return for services provided. Also has a relationship with the merchant acquiring institution whereby they can charge a card belonging to a card scheme provider associated with merchant acquirer, and receive a payment in return.
One of the important things to note, is that the cardholder and the merchant have a relationship with each other (which gives rise to the PoD or foreign equivalent rights) but also each have a relationship with respectively a card issuing and merchant acquiring institution - which gives rise to different rights.
A merchant acquiring institution typically conducts significant credit checks against a merchant - as that institution is taking on a credit risk, as it typically has a contractual obligation to make payments back to the card scheme provider for amounts that may have been charged by the merchant through the facility, but have to be returned under the scheme rules - such as chargebacks. This obligation is not dependent on that institution being able to recover the funds - hence they have a credit risk.
In this situation, where the cardholder potentially has access to the merchant directly (likely to be little joy if insolvent), and via their card issuer, to the scheme rules, and ultimately ending up with the merchant acquiring institution (which will have funds), acting on the route where there is likely to be money should be the first priority. It is not really important to the cardholder if they get the money back effectively from the merchant acquiring institution, which then ends up with the issue of attempting to collect in an administration or liquidation - they have their money, without the hassle of having to deal individually.
Some institutions may try to limit recourse, especially where they have significant exposure as acquiring institutions themselves - as it is the card acquiring institutions that will end up as the debtor of the merchant for chargebacks that end up processed according to the scheme rules. Depending on the arrangements upon which they provided the facility, they may be unsecured, or they may have security of some sort. It will come down to the actual contractual arrangements between the cardholder and the issuing institution, but most issuing institutions would have some obligation to process disputes in line with the scheme rules (imposed by their contractual relationships with the card scheme provider). You may find that suggestions that you should approach the merchant directly are just suggestions, and that if you push hard, they will reluctantly accept the dispute.
Depending on the scheme, and particular arrangement, the one institution may be in multiple roles. The least number of institutions could be only 1 - as in the case of a direct issued Amex card, where Amex is the issuer, scheme provider and acquirer, or there could be even more institutions, where intermediaries sit between issuers / acquirers and schemes. In this case in point, there are likely only two institutions involved - NAB as card issuer, and Amex as scheme provider and merchant acquirer (Amex is the only acquirer for Amex merchant facilities as far as I know).
Whilst the NAB conditions stated do refer to statement due date, the wording also refers explicitly to scheme rules, and to notifying as soon as possible - and in the case of only becoming aware of a provider not delivering a service, that as soon as possible may be very different to the case for a transaction to be disputed for other reasons. In the place of the OP, I would certainly press as hard as possible to lodge a dispute with NAB, even if they claim you are out of time, as it is probably the most likely way of seeing any money back.