This is one of those questions where there really is no exact answer.
The adhesive will stick to the paint. But there is no way to determine
the long-term results of a new tile finish over a painted surface. The
paint can peel, break down or otherwise come loose from the substrate
and the tiles may will also come loose.
A few things I take into consideration when tiling any area are:
1. Weight of tiles on the drywall - I personally will not go moe than 3
feet high on drywall with any tile. If more than 3 feet, replace
drywall with cement board.
2. Wet areas - if tile is being installed in an area where water is
frequent - I use backerboard with a waterproof membrane (Kerdi system