Actually tile is porous. Even 100% vitrified porcelain tiles will absorb some amounts of moisture. Another thing you you need to understand is that uric acid (like any acid) damages grout which is what I think you probably have.
I would guess that the restroom floor is missing or has hairline cracks in the grout or tile and the urine has penetrated under the tile. It is quite common in high traffic commercial bathrooms due to the high humidity found in the restroom combined with the inability of the trapped urine to evaporate (no fresh airflow).
The solution is simple. Many carpet cleaning companies have special equipment to steam clean and deodorize tile floors (didn't know that, huh?:). Once the floor has been cleaned and properly dried use a silicone adhesive to fill any voids and cracks you find in the grout and ceramic tile. Better yet- replace any damaged or loose tiles you find. Then I would consider some heavy skid proof rubber mats to place in these messy areas.
By the way silicone sealers are not widely used in commercial floors because they tend to trap moisture under the floor which can cause more problems than it solves.
If you can't find a carpet cleaner to steam clean the floor for you look in the Yellow Pages for a tile grout restoration company.