I am rebuilding a screened porch and turning it into a four season porch/sunroom. The floor is a 4 inch poured concrete slab over an unheated utility room. The house was built in the late fifties and the slab floor has been painted at least once. I can tell you from working in this area that the paint/coating does seem to be well adhered to the concrete. I was going to have a professional install the tile floor but was told that they could not warrant the job based on the fact that the tile would be applied over a painted slab. My question is.......What would be the proper way to proceed?
Thanks.
Todd

The tile installer is right. Even though nothing may happen, nobody has a crystal ball and the track record of tile over painted floors is not great so he is basing his decision on historical data.
You could do two things.
1. Check around for some membranes that could be put over the paint. I dont know of any offhand but maybe Noble Company or Schluter which makes Ditra. The tile could then be set to the membrane with thinset.

2.Grind the paint off. Some of the more industrial type rental ceneters will rent you a machine that looks like a floor buffing machine. They will sell you the bricks that mount to the underside and grind away everything, plus make the floor more even by removing any high spots. A shop vac hooks up to the outflow port to gather the unbelievable amount of dust that it will create.

Protecto wrap makes a peal and stick anti-fracture menbrane that might work.

http://www.protectowrap.com/cat_floor.php

I ran into another company that has a glue down membrane (vs the thinset type). But I forgot the name.

Also you can get the concrete scrafied.

Shot blasting is one process.

Probably done by company that do concrete resurfacing and restoration work.

My understanding is that there may be a problem down the road with the bond between the paint and the concrete. I am considering laying hardie backer board down over the painted concrete and attaching it using mechanical fasteners. How does this approach sound?

Not a good idea. The Hardi is designed to be nailed or screwed down over a wood subfloor system. You also put thinset under it to fill in the voids between the wood layer and the cement board. The Hardi gets nailed or screwed at 6" intervals around the perimeter and 8" intervals in the body of the board. Thats a lot of screws ($$$) to set into a concrete floor, about 60+ a board. The thinset under the board is IMPERATIVE and the Tapcons or Walldogs ($$$) must be set so the head is flush with the surface of the board unless you want to pour self leveling cement over the whole floor ($$$). After all that the cost of a grinding machine for the day will be under $200, but you will need help to transport it, they are very heavy.