Great post Alberta.
It is a form of particle board.
In certain circumstances, we (BAL) say you can tile onto a floating floor. Our adhesive, BAL fastflex, can be used. The responsibility lies with the tile installer to make sure the floor is rigid enough for a tile application. You can't just stick tiles to any floating floor. It has to be the correct wood, fixed correctly, and more importantly, the insulation under it has to be able to take a tile application. Which all to often it does not.
The problem is, is that most of these floors were installed when the house was originally built, those bathroom floors were then carpeted (Ewwwww!). You can bet your bottom dollar, that insulation is not suitable for a tile.
As you said, you 'can' tile onto a floating floor. And our Fastflex is the adhesive to use. But there are so many variables with them, unless you're 100% sure what the floor is constructed of, don't touch them.