Another thing to point out is that the airlines report supplemental information about airline charges to the credit card companies, which include at least the city pairs on the ticket, the name of the ticketed passenger, the date of travel, the fare class, and the ticket number. These items normally don't appear on a consumer Visa/MasterCard bill, but I do think I've seen them on a corporate card statement before. All those items definitely appear on an Amex statement, even the consumer ones.

I would imagine that for large companies that charge airfare on corporate credit cards, this information gets reconciled to prevent exactly the kind of thing the OP is trying to do from going unnoticed. This is probably one reason why the "one charge for each passenger" rule is in place to start with.