We ran comparative tests on a large number of samples looking at LOI, Walkley Black and Dumas and found that LOI consistently overestimated SOM and that results were more variable. Results are below - we tested for Total Organic Carbon using the Dumas method and converted this to SOM using a factor of 1.724 (assumes carbon comprises 58% of OM hence the straight line). As the 58% is an assumption not a certainty, that is why there is some variability in the Walkley Black method, although it matches up with the Dumas results more closely and parallel. LOI as you can see overestimates, is more variable and the R2 line is not parallel with the other methods. This may be due to carbonates being burnt off or oxidised as you say, and also structural water losses from clays. The Dumas method is a more expensive test, however it's recognised as being more accurate and used a lot more widely in scientific research. NRM now offer it as an analysis method and I'd say the extra cost of good data and information is worth paying.
Another point to consider when comparing OM results is stone content. On gravelly or brashy soils, the same quantity of organic matter inputs would increase the SOM more than it would on a stoneless soil, much in the same way as liming and pH. A farmer I spoke to recently was going to adjust his figures based on stone content % to give a SOM by volume of soil.
