Hi Kevin
We come across this problem on a regular basis, first off you must understand one of the most trusted tools in the cleaning industry (cotton kentucky mops) are one of the most useless tools in the industry as they just push the dirt around the floors being cleaned as when the moisture evaporates the loosened soils just dry back on to the floor surface, this is repeated on a daily basis so the film of soil thats drying back on the floor surface just keeps building up which in turn will make the floor look just like the floors in the pictures.
Using high alkaline cleaning chemicals just add to the problem as they just grind the soils further into the substrate, we have solved this problem for many cleaning contractors, the problem is conformity many cleaners are conformed to using cotton mops and hard surface cleaners which usually have a ph value of betweem 10 to 14
The solution to cleaning hard floors to stop this problem is to use microfiber floor cloths and a hard surface cleaner of between 7.5 to 9 on the ph scale. never use one thats more than 9 on the scale and i promise you will not have this problem again.
we use a microcleaning mop pad to solve these floors as they are far more effective than any pressues washer,scrubber dryer with fiber or nylon pads, if you are deepcleaning large areas we have the microcleaning pads in 16" diameter.
the acid based cleaner we used is foodgrade and will not damage the tiles being cleaned.
Regards
Tadgh