It Took a flight with Swiss and paid EUR 2,300 for it. The receipt I got upon booking online shows about EUR 500. I tried for months to get a proper receipt but so far have not been issued one. This is blocking my travel claim and I am at my wits' end. Do I have a chance of success/is it legal if I start a credit card dispute with Amex for an incorrect amount charged?
Note that triggering a chargeback on a payment that you agreed upon is fraud, and doing so can put you in much more trouble than failing to recover money in your travel claim. For a payment as big as 2300€ I'm pretty sure you had to use something like "3D secure auth" to confirm it, which means your bank will be on the hook for at least part of the sum if they proceed with your chargeback claim. Clearly your bank may not be your friend in this affair.
On the other hand, writing to the airline / travel agent about the discrepancy between the receipt and the amount charged on the credit card, and asking them to rectify this discrepancy is not illegal. This makes it sound like a chargeback will soon follow if they don't react, and is often more effective than just asking for a rectified receipt.
This sounds bizarre and maybe there is some piece of the story missing.
If you booked the ticket directly with Swiss, you should be able to view your trip on their website and download the receipt from there. If the receipt and the amount charge don't match, you can try to contact your credit card company but I doubt it will help. Apparently services were rendered for the agreed upon amount. I don't think they would do a charge-back as "punishment" for a clerical error.
If you booked through a third party, the third party should have issued a receipt. You would need to go through them. It's possible that Swiss has indeed receive only $500 and the $1800 got pocketed by the third party.
So it all depends on who exactly is the entity that charged you and whose name shows up on the credit card statement. Whoever took your money first owes you a receipt.
If all else fails: most companies do have a process to deal with lost or incorrect receipts. It typically involves filing an affidavit (for tax and legal reasons) where you do declare that you indeed incurred this expensive as stated. You can back this up with a copy of the credit card statement and the boarding pass . Your expense department should be able to help with this: people forget or lose receipts occasionally. It's basic human nature.
Specifically addressing the "This is blocking my travel claim" component - does your expense reporting procedure have any allowance for lost receipts etc? Often they'll let you submit the credit card statement (with irrelevant information and other charges redacted for your privacy), along with a signed attestation basically stating that you aren't committing fraud. I would try this if you haven't already, or at least contact someone in the finance department first to get their opinion on the best course of action (again assuming you haven't already tried this, apologies if this seems obvious and you've already done it).
Send a request (via registered mail) to the company you paid (the one whose name appears on amex statement) telling them they charged you more than what you owe attaching the receipt you already have.
If they don't oblige, then proceed with the chargeback request telling AmEx that "wrong amount was charged" attaching the 500€ receipt you already have as a proof.