I have NEVER heard of a tile installer, company, or manufacturer advocate for the use of particle board for use as an underlayment for tile. It's not just about the strength of the particle wood or its deflection factor- Primarily, it's the moisture factor.
Thinset and grout both contain sizable amounts of water. HardiBacker is concerned this moisture will leach into the particle board when you go to set your tile. Water + particle wood = mush!
I don't know about you or others, but I have seen particle board disinegrate by just absorbing the moisture in the air INDOORS.
I do however believe that there is a waterproofing membrane that is available for use on particle wood and can be tiled over. If I remember correctly it is painted on using a roller. I don't remember the name though so you will have to search for it.
If you don't believe that the floor will absorb much water, by all means tile over it. Install your hardibacker with at least 1/4" square notched trowel (3/8" will give you more strength)using a latex modified thinset. Run a fan over the floor to accelerate the drying time of the materials. It will probably work out fine.