I contacted Amex service and was told that Tesla was indeed at fault as they definitely requested 1.000 USD to be charged.
Apparently, all charges made to any credit card worldwide (be it Amex, VISA, Mastercard, etc.) are first converted into USD before being fed into the system. So even if I pay 25 Euros at the local grocery store in Germany via a credit card, those 25 Euros are converted into USD before being charged to the card and then re-converted into Euro for the actual charge. Sounds complicated, but plausible. I am a banker myself and know of quite a lot of similar peculiarites. Though I as yet didn't know that particular one.
Anyway, I contacted Tesla and asked them to rectify the situation. Let's see how this works out.