Friends 1 through 4 make plans to have dinner with friend 5 who is at odds with friend 6. (Friend 5 refuses to discuss exactly what the problem is.) Friend 5 cancels at the last moment. Friend 1 invites friend 6 to join them, making no mention of friend 5's cancellation. Friend 6 is unsure of availability. Friend 3 sends friend 6 an e-mail inviting her along, stating in the e-mail that the original plans included friend 5 who was no longer available so there was a seat at the table for friend 6.
Friend 6 turned down the invite. Friend 6 wants to be included because of a desire for friend 6's company, not as a seat filler so the group can keep their table for 5 reservation.
People can be friends with anyone they want. They don't need to lie and pretend there are no plans when there really are. There is no need to include everyone in every invitation but invitations like this are just plain suck and are quite insulting. Friend 6 doesn't want or need an invitation like this.