I'm not sure what his original source of information was but it seems to borrow ideas from a technique known as freeze-pump-thaw degassing. However, this technique involves freezing the sample and then bringing the sample back to liquid phase, under a vacuum, to enable the gases to be purged. What the effect of freezing and thawing would be, without a vacuum, or a return to liquid phase, I can't say for sure. The vacuum probably just makes the process more efficient, by decreasing the temperature at which the gases evaporate. In which case, the number of freeze/thaw cycles and thaw temperature could be increased to compensate for the lack of vacuum.
However, the return to liquid phase upon thawing may be more important for the purging process than the vacuum, as the gas may remain trapped in a solid, or semi solid. The freezing process should free the gas from it's previously dissolved state but only a return to liquid phase would enable the gas to then congregate together and form bubbles, which would grow in size and buoyancy. Without the liquid phase, the gas may well have become undissolved but still remain locked up as microscopic pores in the sample. This might be why your sample "scrapes up into tiny granules", as it shatters along the millons of microscopic, gaseous pores, set within the sample.
Placing the sample container in luke warm water, during the thaw cycle may enable the oil to become sufficiently liquid to allow the gas to form bubbles, which would then work their way up through the oil as they grow and become more buoyant. If you see bubbles forming and growing with each freeze/thaw cycle, then you know that it is working. Then it's just a case of repeating until all of the bubbles have risen to the surface and no more bubbles are being produced. It may take more than three freeze/thaw cycles, however as that is the number of cycles commonly used in freeze-pump-thaw degassing, which will be considerably more efficient than freeze-thaw purging with no vacuum.