Each tentacle is armed with a venomous stinger and no, clowns are not immuned. Clowns have to prepare their bodies to be able to live among those stinging tentacles...which they do by wiggling through the tentacles building a thicker layer of mucus over their bodie and making themselves smell like the anemone.
Although you may be correct, this has not been scientifically proven. To my knowledge, there are about 4 hypothesis as to how anemonefish avoid being stung by anemones. What you have mentioned is, however, probably the most accepted hypothesis.
One this is for certain...the anemone does not recognize the clownfish and therefore does not fire its stinging cells (nematocysts). HTH