Even if it is on 16 inch centers. If your underlayment is on 24 inch centers, you will need to add additional underlayment.
I believe if you read the instructions on the Hardibacker panels, they recommend 1 1/8 inch minimun underlayment even if 16 inch centers is used.
Hardibacker is an excellent product, but it cannot make up for floors that are too flexible.
If it were my floor, I would add 1/2 inch plywood to the 3/4 inch osb or plywood already there, then put the 1/4 inch Hardibacker over that.
Be sure to use a latex modified grout and motar such as Tec 650 grout and Tec 345 motar.