The body shop states they can beat the problem out. I feel it should be replaced

Yeah the rear floor is carpeted anyways. There is no way they can "replace" the floor unless they cut off the entire rear of the car and replace it. The cost of doing that would be far greater than the value of your IS.

No the floor isn't holding up the car. It can be bent out. You shouldn't see any difference. Although the biggest concern you will have is that you know it was damaged.

Check you policy, if it states,and it should, "pre-loss condition", then the bodyshop needs to replace the area of the floor damaged if it cannot be repaired to pre-loss condition. If you can visually see the floor is still damaged after the bodyshop has done the repair, then this is not pre-loss condition. Call your agent!

Though the floor is change able but it cost so heavy that you can an other car..It should be hard or I must say difficult to bring the floor back in first original shape.