This isn't so much an authorization question as it is a fraud question. The defrauder is taking advantage of the known offline condition to incur a debt that he does not intend to repay.
As a prior answer explained, there are two phases in using a credit card. The first phase is authorization, where the merchant gives the account information and transaction amount to their payment processor. The processor contacts the "issuing bank", who issued the card to the customer. The bank examines the customer's account, makes sure the credit limit is high enough, that the bills are being paid on time, that sort of thing, and creates their approval in the form of a randomly generated number, called an approval code. This number is proof that the authorization took place at the bank, and it is the signal that the bank is willing to accept the risk of this transaction not being paid in the future by the cardholder. The approval code is sent back to the merchant, who prints it on the receipt.
In the second phase, the settlement process is where the merchant sends the day's transactions to the payment processor, and this will include all transactions, whether or not they have approval codes. As a part of settlement, all the money from all those transactions, including the unapproved transactions, will be transferred from the banks to the merchant's account. (The processor brokers these exchanges for a fee.)
The merchant (in this case the airline) may be willing to accept the risk of conducting credit transactions without authorization. An airline would generally have only small transactions for in-flight goods and services (a few dollars for alcoholic drinks, a movie rental, or perhaps a more expensive upgrade to first class.) It's not an amount that puts their business at risk, and the overall amount of money lost to in-flight fraud may be less than the cost of owning in-flight credit authorization terminals. When they accept these transactions they are offline and obviously cannot get an approval code from the bank. At the end of the flight, the airline sends them all to their processor for payment.
Later, the issuing bank will send a bill to the person, asking for him to repay his debt. If he refuses, the bank will look at the transaction and say "this came from Pseudo Payment Processors, who got it from Mythical Airlines, but we never gave them an approval code saying we authorized the charge." The bank will then issue a "chargeback" to the processor, who will in turn pass the chargeback to the airline. A chargeback is simply a request to repay the money. Since they have no approval code as evidence they received the bank's authorization to conduct the transaction, the money comes back out of the airline's pocket, and the airline is not paid for the goods and services they provided in-flight. The airline may then attempt to collect the money another way.
Make no mistake: taking the goods while misrepresenting intent to pay for them meets the legal definition of fraud. The person "at the next table" was a thief.