I think you have missed my point, I said that they could choose what rate they wanted in relation to the statement that they use "customary industry sources" (not source as you have quoted). With a forex spread of over 5-10% variance in some daily trades in recent history you would need to find out the following:
1. What are the sources they use and what market is it based on , for instance the largest currency market trade occurs in London which many of the sources you mentioned do not exclusively quote on, despite it being the bulk of world trades, or perhaps AMex use FxMArketplace as its US based, who knows?
2. What time was the quote taken, for instance when looking at the AUD to USD, the variance in 1 hour a few weeks ago was 4c, historical quotes are usually end of day quotes which can be significantly different to say noon rates at any given interbank location.
Amex do not say which source they use or what time of the day the quote is done for a reason, its called maximising profit!