Alan
OK you have porcelain tiles in black which have a polymer modified (Flexible grout).
It sounds as though the tiler left the grout too long and the floor has been over washed. This has caused several problems. Primarily the grout haze, but moreover because the tiles were not sealed prior to grouting the grout haze will be in all the pits and fissures as well as on the surface. Then because the floor was over washed the polymers in the grout have risen to the surface and formed a protective skin on top of the grout and that is why traditional cleaners are not working. However, all is not lost. So this is the way I would do it:
1. Apply a solvent to the whole surface such as Miracle Epoxy Grout Film Remover or Miracle Mira Strip and agitate. (Be careful because the stripper will strip anything else it comes into contact with). This will break down the polymer skin.
2. Without removing the stripper add in Miracle Heavy Duty Acidic Cleaner and agitate with a Nylon Scrub pad. This will now attack the cementitious properties of the haze itself and clean at the same time.
3. Extract all product (preferably with a wet vac).
4. Rinse and extract again.
Now check the haze remembering that the HDT&G Cleaner will only remove one layer of haze at a time so if there any areas that are thick it may need removing with a mechanical scraper to save time.
Several applications may be required but agitation is the key to this and you do not need to repeat the solvent stage. Finally you may remove all the surface haze and then find you have pinpricks of grout in the pits and fissures of the tile! If this is the case you may need to repeat the cleaning process using a soft brush to get in the pits and fissures and you may even need to resort to Miracle Liquid Poultice A&B to help get it all out.
Finally ONCE DRY seal the area with Miracle 511 Seal & Enhance this will even out all the grout colour and tile colour and also make ongoing maintenance and cleaning easier in the future. Once clean only maintain with a pH Neutral Cleaner to maintain the integrity of the sealer.
Finally I have given you all instructions assuming it is a small area if it is a large area you can do most or all the above with a machine.
Good Luck
Kevin