ABC News reported this week on a "mistake" fare on Alitalia's Japan website through which some people, with the help of a promotional code, were able to secure free or incredibly cheap flights. Initially, the airline was not going to honor tickets.

The airline now says it will honor some of the fares. The only reservations that will not be honored are those that were completely free. So, even if a person using the discount paid just $1, they will be able to fly.

In a statement to ABC News, Alitalia said the error resulted from a system malfunction.

"We offered a worldwide 25 percent discount, with the exception of Japan, where for technical reasons we were forced to create a unique E-Coupon worth 25,000 yen (approximately 250 euro) to be used exclusively for the purchase of flights from Tokyo or Osaka. This redemption rules were clearly stated in the Japanese version of the Facebook offer.

"Unfortunately, due to a malfunction, the system did not recognize the limitation of this unique E-Coupon to be used only on routes from Japan. As a result, the system erroneously allowed the voucher discount of 25,000 yen [about $311] to be used on all routes in Alitalia's global network.

"The news spread rapidly online and in a matter of a few hours our Japanese website reported a dramatic surge in visits and purchase requests from several geographical areas.

This unusual occurrence on the Japanese website triggered a security system alert which, considering the high percentage of number of requests at zero cost, froze all transactions. The promotion's objective was to spur and increase the sale of tickets at a discounted price, and not to issue tickets for free or at a minimal cost."

Brian Kelly, who runs website The Points Guy and was able to book a free flight from Rome to Milan with the promotion code, still won't get his free flight. But he's OK with that.

"In the end, this was an amazing deal and you had to jump in on it quickly," he said. "The old saying, 'If it's too good to be true, it probably is,' isn't always true. Congratulations to those who got in on this and I applaud Alitalia for making a consumer-valued decision. Even though my ticket won't be honored, it's all about looking forward to the next deal."