The "wire mesh" procedure is strongly advised against by the entire mainstream tile industry. It has a very high failure rate and it is one of the cheaper methods. Anyone doing it in that fashion is not current on acceptable methods, get rid of him immediately.
The backerboard is one of the better ways to go but there is still a lot more to the process than deciding between backeboard and some hack-method using wire mesh.
All cement boards MUST BE installed in a fresh bed of thinset mortar. The moisture in the mortar alone can be enough to trigger an expansion of the partical board.
Unfortunately (for you) partical board is also poo-poohed. A tile installation is no place for any type of partical board anywhere in the mix. Simply adding cement board over it doesn't change anything. Partical board will expand and swell under certain moisture conditions (and atmospheric changes) and take the tile installation with it wrecking everything. I guess if your insurance is paid you would have some recourse.
Tile certainly cannot be applied directly to partical board.
The backerboard is one of the better ways to go but there is still a lot more to the process than deciding between backeboard and some hack-method using wire mesh.
Unfortunately (for you) partical board is also poo-poohed. A tile installation is no place for any type of partical board anywhere in the mix. Simply adding cement board over it doesn't change anything. Partical board will expand and swell under certain moisture conditions (and atmospheric changes) and take the tile installation with it wrecking everything. I guess if your insurance is paid you would have some recourse.