If you fell into a volcano, you might not sink in the way you'd imagine.
This video demonstrates what would actually happen if you stepped on lava.
Take your favorite motor oil (I prefer 5W30) at room temperature and fill a small pail. Motor oil at room temperature should have a density of ~920 kg/m3 and viscosity of ~1 Pa-s – this will be your lava. Cut a little fellow out of styrofoam. It has a density of ~300 kg/m3, so it is roughly 1/3 the density of the oil. Now, position your Styroguy on the edge and push him in. Does he sink instantly into the oil? No! So, neither should you in you fall into lava. Now, Stryoguy didn't get the full effect by then proceeding into bursting into flames, which would be your bonus for falling into lava — remember, most of the red-hot lava pictures in movies like likely basaltic lava at ~1,100 to 1,200°C (for comparison, your oven on broil is ~275°C). However, if you're already in a position to fall into lava, you had it coming.
In conclusion: you wouldn't sink, but you would burst into flames.
So, while it's still not a great idea, at least now you have a scientifically accurate reason to be scared.