Proper disposal: Can oil colors spontaneously combust?
Yes, there is still a risk, as the hazard is in the oil; as the oil dries, it emits heat (an exothermic reaction) which, if it's in a pile of other flammable objects--such as other oily rags, papers, etc--can cause them to combust.

From the Wet Canvas forum (the thread also contains some personal experiences with combusting rags):


  Remember it is the linseed oil that heats slightly as it dries (oils dry via a slow combustion process) and if the heat is trapped fire is a possibility, especially combined with highly flammable substances such as solvent. Whether you use solvent or not, soak your oily rags/paper towels in water or spread them out to get air.


And a blog from Mutual of Enumclaw gives an additional citation to rags with oil-based paint on them being a hazard (as well as tips for handling them):


  Simply put, rags that contain residue of oil-based paints and stains, paint thinners, varnishes, or polyurethane can spontaneously combust and catch on fire. Here’s what happens: When oily rags begin to dry, they produce heat. Combined with oxygen they turn into combustible cloths that can quickly cause trouble.


(All emphasis above is mine.)

It is clear that the oil is the risk, and as the paints "straight from the tube" contain oil, it is best to treat them as a risk as much as you would the other items.