The only time I have ever seen fire on stone etc is only ever briefly due to fire spreading (usually from a tree on fire or lightning strike) , never from stationary lava.
The only time I see it is when you have lava source block being still, and blocks being directly next to it, so that the surface of the blocks are at the same level as the top of the lava source block.
Even then, it is not exactly frequent, but I first noticed it while playing vech maps.
The fire don't seem to spread (don't quote me on that), and extinguishes quite fast, but you can and will catch fire if you are standing there.
It seems to happen more regularly when a wooden block that can't burn (chest, crafting table) is one block away, but in these cases, it might be a graphical glitch where the fire is not in the right block.
Then again, it was on 1.2.5 when I last saw this, and I didn't exactly try to see it since then, so it might have changed.