> Such trans fats cannot be consumed by our bodies: their chains are too short to be correctly processed and are too big to pass the mitochondrial membranes.

Oxidizing lipids doesn't introduce chain rotation about their double bonds (which is the difference between cis and trans fats). This change in structure is why trans fats are solid at higher temperature (for the same types of lipids - think the difference between margarine and vegetable oil). The reason trans fats are bad is we can't process them as easily and they seems to accumulate faster than even saturated fats in our blood vessels, mostly because they are synthetic in nature and we don't have specific enzymes optimized to process them.