There is no official mid-market rate, and XE.com is definitely not a source of an interbank rate. The most reliable free source of live wholesale interbank rates is at http://www.truefx.com which closely resemble the rates on EBS, Reuters Spot Matching, Currenex etc. The card networks could do their trades at any time of the day; you don't know when that might be and what the rate might be at that moment.

The rest of your logic is correct.