The nervous system is a communication system. To use a metaphor, cutting off communication to the general’s command bunker doesn’t stop the painful losses his army sustains in battle; it only stops the general from knowing of it.
Pain is subjective as well. Some seek it as a ‘comfort,’ such as teens who cut themselves purposefully. What one person may experience as pain, another might experience as a challenge to push themselves further. Just because you or I wouldn’t call a feeling ‘pain,’ doesn’t mean another doesn’t experience it as ‘pain.’
Cells clearly communicate between each other. Are we as humans so elitist that we can know what other living things ‘feel’? Are we so certain that a cellular version of ‘pain’ is not one of the things communicated between cells?
In short, the organism can suffer whether the ‘head’ knows it or not. Ask Marie Antoinette. Clearly she wasn’t feeling the ‘pain’ of her subjects, when she suggested they eat cake.